Right Angle Triangle Concepts in Geometry

[Music] hi everyone my name is Ravi Prakash and welcome to geometry five okay so from in next few videos we'll discuss about right angle triangle right angle triangle is a super important topic for any exam right including cat and z in Catalan you will see both in two to three questions even in this a cat cat seventeen also right two to three question all your writing and triangle concept right so lots of hidden concepts are there lots of short breaks are there right so everything we will discuss about a right angle triangle in next few videos here on okay so let's start see in right angle triangle the first basically point is you draw any right angle triangle so obviously it's one angle is ninety degrees right substitutes one angle is 90 degree let me draw it now this is a right angle triangle fine writing triangle ABC which is right angled at B now here the orthocenter right two special points here orthocenter answer comes in two right so this circumcenter is basically they made a point of the hypotenuse okay sir in writing a triangle this circumcenter is basically okay let me write here circumcenter is basically they made a point of hypotenuse midpoint of hypotenuse right so again by contraction only one sell draw all those perpendicular bisectors so they will come at exactly made a point of hypotenuse right that is the circumcenter wind right-angle trench and the also center is this point okay the orthocenter at this point that is 90 degree vertex of the right angle triangle so also Center is 90 degree vertex of any right angle triangle right why because also Center will always be intersection point of all those lines which shall form a 90 degree inside a triangle right inside a triangle all those lines which I found form in 90 degree that is the height of the triangle so already we have one CB is C one height of triangle a B is the another height of triangular these two are intersecting at B so obviously if two are intersecting at B the third one will also intersect at be only right obviously that's why B is the also sender ID so in writing a triangle also Center is 90 degree vertex and circumcenter is the midpoint of hypotenuse right so what is the use of having circumcenter ID again B of circumcenter we know so directly I can write okay it's 90 degree circumcenter is made a point of hypotenuse so I can draw a circle keeping this as a center and this has a radius I can draw a circle what a circle Center means a circum circle a circle outside this triangle that will touch the triangle add exactly three points from outside this is circumcircle fine this is also radius this is also radius okay and this is also radius right and since it's the midpoint since this is this is the midpoint so this point will be like this name it my name it BD BD HC right so obviously BD is the median of the triangle BD is the median of the triangle right so what is median so what is median so I can write here BD is equal to median or the trans in that will join the midpoint of a poet side deadline and this equal to circumradius what is circumradius it is half of hypotenuse right that means in any right angle triangle circumradius is what half of hypotenuse and median is equal to circumradius right so this is what is half of hypotenuse always so length of media is equal to half of fiber to use any in any right-handed prandtl very important point okay so is disavow circumcircle right now what ins in real in a circle and India will discuss read about in circle and in radius okay again to very point points in circle and invidious okay now see in so good so in right angle triangle when you draw in circle right in the circle like this inside that means it will touch exactly circle at three points from inside one point to point and three points okay so let me draw a diagram here three points okay fine so at these three points if this self circles will intersect right this is retained in red this a b c is a tangent so always C circumradius we knew we can do it by if that 1/2 of hypotenuse right now this in radius like how I can find in any writing a triangle I can find in radius by that formula area is equal to R into S finding in a dissonant but a very important point we'll discuss here in respect of right angle triangle in terms of hypotenuse right how to find in circle in terms of hypotenuse very point but I'll discuss it try it see for this we know we need to know this probability that in any circle in any circle if from external point I draw two tangents that from external point isn't only two tiny little circle right so this is the tangent let's say PA the tangent and PB is a tangent so from an external point from an external point I can draw only two tangents on the circle like here P and V B right and length of both these tangents should be equal this is a property of circle right from an external point I can draw only two tangents on the circle and then thought both the tangents will be equal right using this property I proved a very important point that in any in any right angle triangle in any right angle triangle in radius is basically semi-perimeter - hypotenuse right in Redis is semi-perimeter - hypotenuse in any right angle triangle in radiuses semi-perimeter - hypotenuse so per important point right and I'll prove it because proved is also work got a good cause afraid so I will prove it see how to prove it now understand so I guess it's circulated named a circle like slate this point is a now okay because conventionally if it is capital a we take this point is small a it is capital B we'll take it a small small B and it is capital C Utica to take it as a small C cut it so this is a B and C so C now this is a radial circle this this is a in circle this is the radius and this is also the radius right this is also the this is centered this radius right so now this hole is what this hole is a and is this length is are this length is our right so what I am left with I am left with this should be how much there should be a minus R this should be a minus R because hole was a this old was a this a minus R right no see name this point D here right I know that C D is equal to a minus R right now C is an external point onto which two tangents are drawn one is C D and name it was CP so like here P has a saddle point so to ten inch around PB and PA here also two tangents are drawn CP and C D so length of board should be equal right this is also equal to 1 this is also equal to e minus R then and this CP is also equal to K minus R right hey - are now here again for internal point right so I did not hear again this will be separate which is also R here this is R so this also are right this is our here now this will be how much how much is AC not it so do you not AC your name Disney against a name shall give some name here let it be Q K let it be Q okay and this foolish thing right this whole length is C here I know this whole latency right this is Q this point is Q okay this point is Q so again this is our okay and this is also R so it is totally see this point should be C minus R right see Q will be equal to C Q will be equal to C minus R so see Q equal to C Q equal to C minus R is nazi q AQ AQ is equal to c minus R this a Q is equal to C - all right this is a Q this is a Q is equal to C minus R and since this is an external point for circle this a Q is a tangent as well as a Peter tangent so by this property length of both tents will be same right so this is a miser this also C minus R so this ap is also C minus C minus R so I can write directly that I can write here that see now this whole AC is equal to I know this whole length is B right this whole AC is equal to B that I know so if whole AC is equal to B so in that case I can write B is equal to B is equal to a minus R plus C minus R right that is hypotenuse is equal to a minus R that is this length plus same as R this inside this hole is equal to B so I can write here that okay so B is equal to what now so B is equal to a plus C minus tu1 fine or I can write from here or two R is equal to B 2 r is equal to a plus C minus me red 2 R is equal to a plus C minus B now what is our here R is equal to a plus C minus B by 2 so R is equal to a plus C minus B by 2 and I can write like this this R I can write like this here see this R is equal to this R is equal to a plus C minus B by 2 it can be written as a plus C plus B by 2 minus B correct so what is a plus C plus B by 2 so a plus this whole this whole length is B right this whole length is B this whole length is a this whole length is C so a plus C plus B is the perimeter by 2 is what's a perimeter what is beer hypotenuse this is semi-perimeter and this is hypotenuse right that's why I told any radius what any radius semi-perimeter - hypotenuse so super you point point in this is semi perimeter - hypotenuse right later on we will do questions on it rate will do coaches are fine ok so 3-point point next thing here next thing directly find again see so now we will discuss about three of the we will discuss about few of the Pythagorean triplets right again a very important concept it is Pythagorean triplets okay okay so Pythagorean triplets right now what are water Pythagorean triplets numbers satisfying Pythagoras theorem right what is possible sorry so Pythagoras theorem is basically e this e P and C this is 90 degree so what is pi theorem c square is equal to a square plus B Square C square is equal to a square plus B Square this is nothing but Pythagoras theorem Pythagoras theorem right now all the numbers which satisfy this theorem are called Pythagorean triplets are called a Pythagorean triplets right but they were giving huge importance in quant in especially in geometry and in all areas Am's right maintains they would added questions if you could find it it is very easy right I'll tell you all the methods to find pressure on triplets right so see some basic examples right some pc+ billets are basically some most bc puzzle interprets three four five is the most basic Python interpreter ID and a lot of time its application is in option exam right so what is three four five basically that basically means that always right when C square is equal to a square plus B square fine so basically if you have keep a as three and B as four so C will come it adds come as five right C will commit and come and come as five fine so 3 square plus four square equal to 5 is satisfying the Pythagorean triplet so it is finally 5 so I am right by third standard is fight the Gordon triplet and then opponent one is 5 12 13 ok 5 12 13 that means if it is 4:30 square is equal to 5 squared L 12 spaces are in a Python internet right so like this how many templates move is basically to remember C first I'll tell you most common triplets remember 8 5 12 13 then 7 24 25 then eight 15 17 then nine forty forty one and then twenty twenty one twenty nine right these are the most of basic triplets that had that have to be that can be off in exams right more six most basic triplets you can remember it always right and because if the quotient is an exam 99% is chance is there that it will be one of these among the six triplets one of the six triplets right if your questions are right I'll tell you because these are not the only numbers right they've any multiples so this is a basic triplets idea written these are the most basic so this is basic I should write like this a lot I should we should call it these are basic Pythagorean triplet okay this six are most basic and most commonly used by different triplet okay now suppose the the question is the sides of a triangle are is given that sides of a triangle are sides of a triangle are right 18 24 and 30 centimeter and they owed us further solve the question right let's so let's find it's as you assume that in this question to find the area of triangle so you have to find the area of triangle right so you can find commonly which is formula area equal to root under SN to s minus a into S minus B into X minus the anytime you can find to find that formula right but this 18 24 30 if you could observe it is nothing but it is derived from three four five right how to find it what you do you directly take the HCF out okay you directly take the HTF out what is SC of here six so take the highest common factor out right so they take the six out from here you look like okay 3 6 into 3 18 four and five right so this is basically nothing but 6 into 3 4 5 triangle right it says 6 times of 3 4 5 triangle right so again so we know that this is a bit appropriate so this is a right angle this is a right angle another way under together number right sides of a triangle is given that sides of a triangle are 15 36 and 39 okay now you have to find the area of the triangle here right and and if you don't recognize it is a right angle triangle and finding is very difficult right ear a equal to root or dead s into S minus a into S minus B into S minus C very difficult to do right but it is emitted then lot easier if you don't resist recognize this 15 36 39 now again how do how to know that from which basic template this is derived if it if at all it is a right angle triangle how to know it right so first thing we should do is to check it is a right angle triangle or not right so check check it is a right angle triangle or not always right whenever this random sides of triangle given always a check it is reading and writing the triangular note because if it is riding on a triangle things will become very easy right so 15 36 39 so how to how to chip take the common factor out and I can see your 3 is the comment out and all these numbers write it in 53 out so take 3 out 5 12 and 13 is there so I know that 5 today's a busy pattern interpret right or it is much easy to check now if if you can apply Patterson over here is much easier 830 square is equal to PI P squared is 12 square so check here is much easy rather than checking here right that 39 you square is equal to 15 is square plus 36 square right now it's a huge task cavity third is square Kelvin if it is square then 50 is 50 50 square this thing LHS is equal to RHS or not right so not a good way rate so always in some random big numbers are given always take the common factor out and check it is a right angle triangle er no right so to remember those six basic pythor interprets right now after that how to find how to find or how to form write how to formation on again idea formation of Pythagorean triplets formation of Pythagorean triplets how do you form by to double it right so I'll tell you a good shortcut here how to find it see note triplets can be found from one or two note triplets can be formed from one or two okay you start from three or I can I get I should really write it let's find for all the odd numbers let's find for all the odd numbers first okay for order we'll see what you need to do here is you're suppose you are trying to form a triplet with three so it's like like this something is square plus something is square is equal to this is square right like I should write here a square plus B square is equal to C square now you can take these numbers out right start from three I know three squared is nine right I know three squared is nine if three squared is nine what you do you divide 9 by 2 3 square you divide 9 by 2 9 it is about 4.5 now 4.5 is the average of red is in the middle of which 2 positive numbers the 4.5 is in the middle of or is the average of which 2 conservative numbers 4 and 5 right in place for you can base 5 here so 3 4 5 is a pythor underplayed 3 4 5 is a white they got interpret right another let's take a five-year if I put 5 here so 5 is square is 25 okay so 20 so I should write 3 4 5 5 is a Python interpreter in this case now if I'm if I'm trying to falter played with 5 5 v square is 125 right so v square is 25 25 1/2 is 12.5 or 12.5 lies between which two ones consecutive numbers 12 and 13 right that means place here 12 and place here 13 say to satisfy raid and I can write 5 12 13 is a price or interpret tried another text on a number take like 11 so 11 is square right what is even trying to form a triplet with 11 what is 11 a square it is 121 121 half is what sixty point five sixty point comes four sixty point five comes between what comes between 60 and 61 so place sixty and sixty one year correct like this uniform with any odd number I'd get forward nine awesome put nine here what is 9 square 81 what is it 81 half 40.5 40.5 lighted in what so 40.5 lies between 40 and 41 in place 14 in place 41e right so very good concept for Pythagoras theorem right so 11 60 61 is a Pythagorean template right 9 40 41 so you can see that with all these odd numbers right we can form a triplet and here the numbers will be consecutive integers right constitutive integer 1213 60 61 40 41 consecutive but because what we are doing is calculating the square and dividing way too so always if an odd number is square divided by 2 so answer to always something 0.5 like here 9 squared is 81 by 2 40.5 40 point finalized in which two positive integers 1414 right so basically an atom is what we need to do if square of a number is square of a number and then divide by 2 right like if I want to form a triplet with five square it to 25/2 12.5 so 12 and 13 are the other other other part of the triplet right so this is for one can obviously feel that is for one kind of this pi-theorem right it would not be always there very ugly there will be lot other card numbers off for this pythor interprets obviously because this is so all four odd numbers right now I can do for even numbers I can do okay for even oversleep okay let's - for even numbers how to form Pythagorean to play to it even in verse 3 for even numbers again a square plus B Square equal to C square now you place an even number F for I told you 1 & 2 which we can't form a tab little 1 & 2 so first is for you right now Square it 4 squared 16 so in even number scale going to do you take a square of number and then you divide by 4 right so 4 square is 16 so 16 by 4 okay so 4 squared is 16 so 16 by 4 is 4 okay and 4 is the average of which two numbers which to concept of into this 3 and 5 right so what you need to take after dividing inaudible or sorta dividing by 2 that result is algorithm which two positive integers and in even numbers also this average is a result of which to convert consecutive integers right so which two consecutive integers so force a three and five right so three and five I can play C at 3 and 5 I can place here so I can forward to great three four five from here right check another odd number another he be number let's take up eight right so again what is a t-square so a t-square is sixty four sixty four by four is what 16 now 16 is the average of which two cons between dinners 15 and 17 right so 15 and 17 I can place a right so that means 8 to 15 17 is a Python triplet I getting any but I can take 12 also get to it first 12 is 12 square 144 144 by 4 144 by 4 that is 36 36 is the average of the I agree which two cons would even do this 35 and 37 right so 25 I can place here and 37 I can place here right so 12 35 37 so you can form all the triplets by this method right all four even numbers and all four or doubles you can easily form the Pythagorean triplets right very important and sure to reimpose those six triplets three four five five twelve thirteen seven twenty four twenty five eight fifteen seventeen nine forty forty-one Twenty twenty one twenty nine right six very very commonly used triplets it to betray right okay now let's do a question here let's do a question here sides of a triangular sides of a triangle are three four and five fine what is his circumradius and what is the inner radius right it should be very easy by now because I know three four five is a Pythagorean triplets it is a right angle triangle of course so in right angle triangle in right angle triangle ABC this is 5 this is 3 this is 4 4 this circumstance circumradius is basically about half of hypotenuse right you got this is Center is what Center is d4 circumcircle for circumcircle center is the midpoint of hypotenuse so this is also on this is also alright so that ligament circumradius is what is half of hypotenuse that is 5 by 2 that is 2.5 okay but is any radius so see any radius are injected by two things right any radius can be calculated by first area is equal to R into this okay so I can get areas what half into 3 into 4 what is our in our any two calgrove calculate what is this ASSA perimeter what is a permitted three plus four plus five twelve 12 by 2 6 so our into 6 okay so therefore you get R is equal to 1 fine or you can get R by what I know that what is in radius semi-perimeter - hypotenuse right we just discuss it we just discussed it in the last video and we aquatic proof also it right in that discussion so what is R equal to s are indeed his word indeed he says semi-perimeter - hypotenuse right for the same parameter here 3 plus 4 plus 5 by 2 that is 6 - hypotenuse that is 5 6 - 5 1 right so both way in method 2 and 101 in both the method is the applet in radius of any right angled triangle right okay thank you we will discuss the questions in next video price related to right angle triangle lots of good concepts digital left and questions below ok so watch the next video thank you you

[Music] hi everyone my name is Ravi Prakash and welcome to geometry five okay so from in next few videos we&#39;ll discuss about right angle triangle right angle triangle is a super important topic for any exam right including cat and z in Catalan you will see both in two to three questions even in this a cat cat seventeen also right two to three question all your writing and triangle concept right so lots of hidden concepts are there lots of short breaks are there right so everything we will discuss about a right angle triangle in next few videos here on okay so let&#39;s start see in right angle triangle the first basically point is you draw any right angle triangle so obviously it&#39;s one angle is ninety degrees right substitutes one angle is 90 degree let me draw it now this is a right angle triangle fine writing triangle ABC which is right angled at B now here the orthocenter right two special points here orthocenter answer comes in two right so this circumcenter is basically they made a point of the hypotenuse okay sir in writing a triangle this circumcenter is basically okay let me write here circumcenter is basically they made a point of hypotenuse midpoint of hypotenuse right so again by contraction only one sell draw all those perpendicular bisectors so they will come at exactly made a point of hypotenuse right that is the circumcenter wind right-angle trench and the also center is this point okay the orthocenter at this point that is 90 degree vertex of the right angle triangle so also Center is 90 degree vertex of any right angle triangle right why because also Center will always be intersection point of all those lines which shall form a 90 degree inside a triangle right inside a triangle all those lines which I found form in 90 degree that is the height of the triangle so already we have one CB is C one height of triangle a B is the another height of triangular these two are intersecting at B so obviously if two are intersecting at B the third one will also intersect at be only right obviously that&#39;s why B is the also sender ID so in writing a triangle also Center is 90 degree vertex and circumcenter is the midpoint of hypotenuse right so what is the use of having circumcenter ID again B of circumcenter we know so directly I can write okay it&#39;s 90 degree circumcenter is made a point of hypotenuse so I can draw a circle keeping this as a center and this has a radius I can draw a circle what a circle Center means a circum circle a circle outside this triangle that will touch the triangle add exactly three points from outside this is circumcircle fine this is also radius this is also radius okay and this is also radius right and since it&#39;s the midpoint since this is this is the midpoint so this point will be like this name it my name it BD BD HC right so obviously BD is the median of the triangle BD is the median of the triangle right so what is median so what is median so I can write here BD is equal to median or the trans in that will join the midpoint of a poet side deadline and this equal to circumradius what is circumradius it is half of hypotenuse right that means in any right angle triangle circumradius is what half of hypotenuse and median is equal to circumradius right so this is what is half of hypotenuse always so length of media is equal to half of fiber to use any in any right-handed prandtl very important point okay so is disavow circumcircle right now what ins in real in a circle and India will discuss read about in circle and in radius okay again to very point points in circle and invidious okay now see in so good so in right angle triangle when you draw in circle right in the circle like this inside that means it will touch exactly circle at three points from inside one point to point and three points okay so let me draw a diagram here three points okay fine so at these three points if this self circles will intersect right this is retained in red this a b c is a tangent so always C circumradius we knew we can do it by if that 1/2 of hypotenuse right now this in radius like how I can find in any writing a triangle I can find in radius by that formula area is equal to R into S finding in a dissonant but a very important point we&#39;ll discuss here in respect of right angle triangle in terms of hypotenuse right how to find in circle in terms of hypotenuse very point but I&#39;ll discuss it try it see for this we know we need to know this probability that in any circle in any circle if from external point I draw two tangents that from external point isn&#39;t only two tiny little circle right so this is the tangent let&#39;s say PA the tangent and PB is a tangent so from an external point from an external point I can draw only two tangents on the circle like here P and V B right and length of both these tangents should be equal this is a property of circle right from an external point I can draw only two tangents on the circle and then thought both the tangents will be equal right using this property I proved a very important point that in any in any right angle triangle in any right angle triangle in radius is basically semi-perimeter - hypotenuse right in Redis is semi-perimeter - hypotenuse in any right angle triangle in radiuses semi-perimeter - hypotenuse so per important point right and I&#39;ll prove it because proved is also work got a good cause afraid so I will prove it see how to prove it now understand so I guess it&#39;s circulated named a circle like slate this point is a now okay because conventionally if it is capital a we take this point is small a it is capital B we&#39;ll take it a small small B and it is capital C Utica to take it as a small C cut it so this is a B and C so C now this is a radial circle this this is a in circle this is the radius and this is also the radius right this is also the this is centered this radius right so now this hole is what this hole is a and is this length is are this length is our right so what I am left with I am left with this should be how much there should be a minus R this should be a minus R because hole was a this old was a this a minus R right no see name this point D here right I know that C D is equal to a minus R right now C is an external point onto which two tangents are drawn one is C D and name it was CP so like here P has a saddle point so to ten inch around PB and PA here also two tangents are drawn CP and C D so length of board should be equal right this is also equal to 1 this is also equal to e minus R then and this CP is also equal to K minus R right hey - are now here again for internal point right so I did not hear again this will be separate which is also R here this is R so this also are right this is our here now this will be how much how much is AC not it so do you not AC your name Disney against a name shall give some name here let it be Q K let it be Q okay and this foolish thing right this whole length is C here I know this whole latency right this is Q this point is Q okay this point is Q so again this is our okay and this is also R so it is totally see this point should be C minus R right see Q will be equal to C Q will be equal to C minus R so see Q equal to C Q equal to C minus R is nazi q AQ AQ is equal to c minus R this a Q is equal to C - all right this is a Q this is a Q is equal to C minus R and since this is an external point for circle this a Q is a tangent as well as a Peter tangent so by this property length of both tents will be same right so this is a miser this also C minus R so this ap is also C minus C minus R so I can write directly that I can write here that see now this whole AC is equal to I know this whole length is B right this whole AC is equal to B that I know so if whole AC is equal to B so in that case I can write B is equal to B is equal to a minus R plus C minus R right that is hypotenuse is equal to a minus R that is this length plus same as R this inside this hole is equal to B so I can write here that okay so B is equal to what now so B is equal to a plus C minus tu1 fine or I can write from here or two R is equal to B 2 r is equal to a plus C minus me red 2 R is equal to a plus C minus B now what is our here R is equal to a plus C minus B by 2 so R is equal to a plus C minus B by 2 and I can write like this this R I can write like this here see this R is equal to this R is equal to a plus C minus B by 2 it can be written as a plus C plus B by 2 minus B correct so what is a plus C plus B by 2 so a plus this whole this whole length is B right this whole length is B this whole length is a this whole length is C so a plus C plus B is the perimeter by 2 is what&#39;s a perimeter what is beer hypotenuse this is semi-perimeter and this is hypotenuse right that&#39;s why I told any radius what any radius semi-perimeter - hypotenuse so super you point point in this is semi perimeter - hypotenuse right later on we will do questions on it rate will do coaches are fine ok so 3-point point next thing here next thing directly find again see so now we will discuss about three of the we will discuss about few of the Pythagorean triplets right again a very important concept it is Pythagorean triplets okay okay so Pythagorean triplets right now what are water Pythagorean triplets numbers satisfying Pythagoras theorem right what is possible sorry so Pythagoras theorem is basically e this e P and C this is 90 degree so what is pi theorem c square is equal to a square plus B Square C square is equal to a square plus B Square this is nothing but Pythagoras theorem Pythagoras theorem right now all the numbers which satisfy this theorem are called Pythagorean triplets are called a Pythagorean triplets right but they were giving huge importance in quant in especially in geometry and in all areas Am&#39;s right maintains they would added questions if you could find it it is very easy right I&#39;ll tell you all the methods to find pressure on triplets right so see some basic examples right some pc+ billets are basically some most bc puzzle interprets three four five is the most basic Python interpreter ID and a lot of time its application is in option exam right so what is three four five basically that basically means that always right when C square is equal to a square plus B square fine so basically if you have keep a as three and B as four so C will come it adds come as five right C will commit and come and come as five fine so 3 square plus four square equal to 5 is satisfying the Pythagorean triplet so it is finally 5 so I am right by third standard is fight the Gordon triplet and then opponent one is 5 12 13 ok 5 12 13 that means if it is 4:30 square is equal to 5 squared L 12 spaces are in a Python internet right so like this how many templates move is basically to remember C first I&#39;ll tell you most common triplets remember 8 5 12 13 then 7 24 25 then eight 15 17 then nine forty forty one and then twenty twenty one twenty nine right these are the most of basic triplets that had that have to be that can be off in exams right more six most basic triplets you can remember it always right and because if the quotient is an exam 99% is chance is there that it will be one of these among the six triplets one of the six triplets right if your questions are right I&#39;ll tell you because these are not the only numbers right they&#39;ve any multiples so this is a basic triplets idea written these are the most basic so this is basic I should write like this a lot I should we should call it these are basic Pythagorean triplet okay this six are most basic and most commonly used by different triplet okay now suppose the the question is the sides of a triangle are is given that sides of a triangle are sides of a triangle are right 18 24 and 30 centimeter and they owed us further solve the question right let&#39;s so let&#39;s find it&#39;s as you assume that in this question to find the area of triangle so you have to find the area of triangle right so you can find commonly which is formula area equal to root under SN to s minus a into S minus B into X minus the anytime you can find to find that formula right but this 18 24 30 if you could observe it is nothing but it is derived from three four five right how to find it what you do you directly take the HCF out okay you directly take the HTF out what is SC of here six so take the highest common factor out right so they take the six out from here you look like okay 3 6 into 3 18 four and five right so this is basically nothing but 6 into 3 4 5 triangle right it says 6 times of 3 4 5 triangle right so again so we know that this is a bit appropriate so this is a right angle this is a right angle another way under together number right sides of a triangle is given that sides of a triangle are 15 36 and 39 okay now you have to find the area of the triangle here right and and if you don&#39;t recognize it is a right angle triangle and finding is very difficult right ear a equal to root or dead s into S minus a into S minus B into S minus C very difficult to do right but it is emitted then lot easier if you don&#39;t resist recognize this 15 36 39 now again how do how to know that from which basic template this is derived if it if at all it is a right angle triangle how to know it right so first thing we should do is to check it is a right angle triangle or not right so check check it is a right angle triangle or not always right whenever this random sides of triangle given always a check it is reading and writing the triangular note because if it is riding on a triangle things will become very easy right so 15 36 39 so how to how to chip take the common factor out and I can see your 3 is the comment out and all these numbers write it in 53 out so take 3 out 5 12 and 13 is there so I know that 5 today&#39;s a busy pattern interpret right or it is much easy to check now if if you can apply Patterson over here is much easier 830 square is equal to PI P squared is 12 square so check here is much easy rather than checking here right that 39 you square is equal to 15 is square plus 36 square right now it&#39;s a huge task cavity third is square Kelvin if it is square then 50 is 50 50 square this thing LHS is equal to RHS or not right so not a good way rate so always in some random big numbers are given always take the common factor out and check it is a right angle triangle er no right so to remember those six basic pythor interprets right now after that how to find how to find or how to form write how to formation on again idea formation of Pythagorean triplets formation of Pythagorean triplets how do you form by to double it right so I&#39;ll tell you a good shortcut here how to find it see note triplets can be found from one or two note triplets can be formed from one or two okay you start from three or I can I get I should really write it let&#39;s find for all the odd numbers let&#39;s find for all the odd numbers first okay for order we&#39;ll see what you need to do here is you&#39;re suppose you are trying to form a triplet with three so it&#39;s like like this something is square plus something is square is equal to this is square right like I should write here a square plus B square is equal to C square now you can take these numbers out right start from three I know three squared is nine right I know three squared is nine if three squared is nine what you do you divide 9 by 2 3 square you divide 9 by 2 9 it is about 4.5 now 4.5 is the average of red is in the middle of which 2 positive numbers the 4.5 is in the middle of or is the average of which 2 conservative numbers 4 and 5 right in place for you can base 5 here so 3 4 5 is a pythor underplayed 3 4 5 is a white they got interpret right another let&#39;s take a five-year if I put 5 here so 5 is square is 25 okay so 20 so I should write 3 4 5 5 is a Python interpreter in this case now if I&#39;m if I&#39;m trying to falter played with 5 5 v square is 125 right so v square is 25 25 1/2 is 12.5 or 12.5 lies between which two ones consecutive numbers 12 and 13 right that means place here 12 and place here 13 say to satisfy raid and I can write 5 12 13 is a price or interpret tried another text on a number take like 11 so 11 is square right what is even trying to form a triplet with 11 what is 11 a square it is 121 121 half is what sixty point five sixty point comes four sixty point five comes between what comes between 60 and 61 so place sixty and sixty one year correct like this uniform with any odd number I&#39;d get forward nine awesome put nine here what is 9 square 81 what is it 81 half 40.5 40.5 lighted in what so 40.5 lies between 40 and 41 in place 14 in place 41e right so very good concept for Pythagoras theorem right so 11 60 61 is a Pythagorean template right 9 40 41 so you can see that with all these odd numbers right we can form a triplet and here the numbers will be consecutive integers right constitutive integer 1213 60 61 40 41 consecutive but because what we are doing is calculating the square and dividing way too so always if an odd number is square divided by 2 so answer to always something 0.5 like here 9 squared is 81 by 2 40.5 40 point finalized in which two positive integers 1414 right so basically an atom is what we need to do if square of a number is square of a number and then divide by 2 right like if I want to form a triplet with five square it to 25/2 12.5 so 12 and 13 are the other other other part of the triplet right so this is for one can obviously feel that is for one kind of this pi-theorem right it would not be always there very ugly there will be lot other card numbers off for this pythor interprets obviously because this is so all four odd numbers right now I can do for even numbers I can do okay for even oversleep okay let&#39;s - for even numbers how to form Pythagorean to play to it even in verse 3 for even numbers again a square plus B Square equal to C square now you place an even number F for I told you 1 &amp; 2 which we can&#39;t form a tab little 1 &amp; 2 so first is for you right now Square it 4 squared 16 so in even number scale going to do you take a square of number and then you divide by 4 right so 4 square is 16 so 16 by 4 okay so 4 squared is 16 so 16 by 4 is 4 okay and 4 is the average of which two numbers which to concept of into this 3 and 5 right so what you need to take after dividing inaudible or sorta dividing by 2 that result is algorithm which two positive integers and in even numbers also this average is a result of which to convert consecutive integers right so which two consecutive integers so force a three and five right so three and five I can play C at 3 and 5 I can place here so I can forward to great three four five from here right check another odd number another he be number let&#39;s take up eight right so again what is a t-square so a t-square is sixty four sixty four by four is what 16 now 16 is the average of which two cons between dinners 15 and 17 right so 15 and 17 I can place a right so that means 8 to 15 17 is a Python triplet I getting any but I can take 12 also get to it first 12 is 12 square 144 144 by 4 144 by 4 that is 36 36 is the average of the I agree which two cons would even do this 35 and 37 right so 25 I can place here and 37 I can place here right so 12 35 37 so you can form all the triplets by this method right all four even numbers and all four or doubles you can easily form the Pythagorean triplets right very important and sure to reimpose those six triplets three four five five twelve thirteen seven twenty four twenty five eight fifteen seventeen nine forty forty-one Twenty twenty one twenty nine right six very very commonly used triplets it to betray right okay now let&#39;s do a question here let&#39;s do a question here sides of a triangular sides of a triangle are three four and five fine what is his circumradius and what is the inner radius right it should be very easy by now because I know three four five is a Pythagorean triplets it is a right angle triangle of course so in right angle triangle in right angle triangle ABC this is 5 this is 3 this is 4 4 this circumstance circumradius is basically about half of hypotenuse right you got this is Center is what Center is d4 circumcircle for circumcircle center is the midpoint of hypotenuse so this is also on this is also alright so that ligament circumradius is what is half of hypotenuse that is 5 by 2 that is 2.5 okay but is any radius so see any radius are injected by two things right any radius can be calculated by first area is equal to R into this okay so I can get areas what half into 3 into 4 what is our in our any two calgrove calculate what is this ASSA perimeter what is a permitted three plus four plus five twelve 12 by 2 6 so our into 6 okay so therefore you get R is equal to 1 fine or you can get R by what I know that what is in radius semi-perimeter - hypotenuse right we just discuss it we just discussed it in the last video and we aquatic proof also it right in that discussion so what is R equal to s are indeed his word indeed he says semi-perimeter - hypotenuse right for the same parameter here 3 plus 4 plus 5 by 2 that is 6 - hypotenuse that is 5 6 - 5 1 right so both way in method 2 and 101 in both the method is the applet in radius of any right angled triangle right okay thank you we will discuss the questions in next video price related to right angle triangle lots of good concepts digital left and questions below ok so watch the next video thank you you

Transcript for:Right Angle Triangle Concepts in Geometry

Transcript for:
Right Angle Triangle Concepts in Geometry