[Music] hi my name is Ravi Prakash and welcome to six plus or geometry okay so fill containers continue of the fifth class favored in writing triangle all those Pythagorean triplets and all right we did now few questions will do okay so see these are trying earlier sites are given as 15 20 and 25 a D is the perpendicular on the side 25 so I need to find the sum of any radius of trundles abd and triangle a DS okay let's solve it right for see again sides of triangle are 15 20 and 25 right so once you take the common factor out that is 5 so it becomes a 3 4 500 3 4 5 triangle right that means it is a right angle triangle so it is a right angle triangle standard angle triangle 25 right longest side is the hypotenuse so 25 should be the hypotenuse right this should be 90 degree this should be negative right because angle opposite to hypotenuse is for 90 degree fine this is 90 degree so now so for this triangle right to get this get D to get D in radius for triangle abd so for this I need to get is in radius red in a radius for this I I need to have the all three I need to have all three sides why because what is n radius semi-perimeter - hypotenuse righty you calculate by either way area equal to R into S or by in Redis is what's a perimeter by - hypotenuse in both these cases I need 7 perimeter semi-perimeter means what all three sides I need right all three sides I need so I already 150 is known so I should get get DK i should calculate ad here so I should for it calculate AED okay sorry should first calculate ad in okay so now what is ad here so ad is the height of the triangle and height can be easily calculated by calculator to calculate by a very good concept because area since it is a right angle triangle so area is the what is the area of triangle half into 15 into 20 so the area of triangle is what 150 so I can equate area of triangle is 152 half into height into base half into height into base right that is half into height into 25 therefore height is equal to solve it you get height as 12 therefore ad is equal to 12 circuit ad is equal to 12 height is 12 year right so in any triangle it is a good concept actually in any triangle if all three sides are known so if all three sides are known then you can get the area of triangle also the area of triangle so and then you can get the height of triangle all right if all three sides are known dedicatedly area of triangle as well as height of triangle you can get fine okay so ad ad equal to 12 I got here so this is 15 is 12 so by PI theorem BD will be what 9 will be 9 different what is BD so BD will be equal to 215 a square minus I am so rule take 81 so route 81 is about 9 so beauty will be equal to 9 ok so this is the so this will be what about 16 because whole is 25 right so you have to time is now one triangle is this triangle is nine twelve fifteen and this triangle is 200 1620 and I need to find the inner radius of both this triangle side what is the in radius of both this triangle sides now I can do it directly or sort is again reduced semi-perimeter - hypotenuse right so here it is what same parameter - hypotenuse what is a very meter here 9 plus 12 plus 15 that is 36 by 2 DT 18 minus 15 that is 3 so r1 is 1/3 okay let's call to call it r1 now for second one in radius I need to find it's 3 to be called r2 until it is what is r2 again semi-perimeter - hypotenuse what is a valued area 12 16 20 triangle so 12 16 20 triangle so 12 plus 16 28 plus 20 48 48 by 2 24 is a parameter - hypotenuse 20 so 24-20 it becomes 4 therefore I need to find R 1 plus R 2 that is 3 plus 4 for example set answer is 7 so 7 is answer for this question right 7 is the answer for this question ok now next question will do okay so the next question is these are it rectangle ABCD which sides be given 9s 9 and 12 find the distance between the in centers of triangle ABC and triangle ABC okay let's read this question pause this video 5 minutes and solve it try it try it try this question ok we will solve now see now it is find the distance between in centers of triangle ABC and triangle ABC right now see if we are ready tried for five minutes then what is the problem you will face is many people will make this two circles coinciding with each other okay many people will make this two circles coinciding with each other that means or maybe just it turn it turn le touching with each other right that's why I didn't try we will try it you will know this mistake what will take you can meet right so I need to find distance between ins and decide now why how I know that these two circles will be apart and they want to be coinciding or they won't be touching each other right see basically it's a fund of normal common sense fun to see in any square right if it is square is square if I draw a diagonal this is an absolute it to equal area as well as by symmetry also everything this side decide is equal this is this is equal right other equal only so any circle I make here it will be like making here in fabric here these two will be touching each other at this point okay but as soon as I move from square to rectangle right so to happen if it is a rectangle now so this circle will start we start hitting apart from each other right this way like this logically female diagram like this because for in circle you need to touch the circle at three points right at three point in a circle right so for touching it now the circle will keep on going apart the more is a difference between length and bigger rectangle right so circle will keep on winning apart right that's the fund I hear so that's why they will not touch each other you go it's a rectangular since it says it is a rectangle into angle each angle is 90 degree each angle is 90 degree right so in this case and a poet sides of rectangle are equal this is mine this is mine this is 12 this is 12 okay right now I need to find it distance between in centre let's join this line okay so I need to find this length call it PQ right now see this is very important for under actually in whole geometry this is nothing but is this is an application of Pythagoras theorem right now what did how in how it is an application of Pythagoras theorem because whenever you have to find distance between any two points side whenever you need to find distance between any two points distance between any two points like this right P and Q and these two are neither horizontal nor vertical neither completely horizontal nor completely vertical right so if this is not the case then this this is solved by Pythagoras theorem right notice fathom so if these taupe is distance between these two points I need to find out the length of the line I need to find the vertical distance between these two and Horace horizontal distance between these two right so I would I need to find this length and this length since this is horizontal this is sorry since this is horizontal it is vertical so both will meet an angle of 20 degree right so this is a this is B so this is will be what root under a square plus B Square by five over seven right so very important point is this so whenever you have to find the length of a line which is neither horizontal nor vertical right it is like some word tilted blindly get the horizontal part water part get the vertical part end solved by Pythagoras theorem right so here also I need to from PQ I need to draw a horizontal line and a vertical line right to form this angle is 90 degree right but many of you can argue here that why this angle is 90 degree right means why it is necessary that it is absolutely passing through here only okay why it can't pass like this surrounding right it can pass like this also it can be Auto J circle and it can pass like this also so why not like this right so okay we prove it right we will prove it why not like this okay see what is the radius of the circle so since this is nine this is 12 is 90 degree so by pi theorem this AC will be 15 okay and in just last question we saw that for a nine twelve fifteen triangle what is the inner radius say beta - hypotenuse so it comes out to be how much it is three this radius is three okay so when this radius is three this diameters become six this is three plus a 6 right this whole is nine this whole is nine the diameter is 6 the radius is three diameter is 6 this also becomes three right similarly while coming to this side again this radius is three here that means you can see this round rectangle from this base of rectangles CD from CD P is also at a distance of three units right and this this point right rename this point as let's say our R is altered at a distance of three units what is on this endpoint of this circle right this is a this is also at a distance of three units that means these two are in a sprint line that means if I draw these two lines this will be absolutely tangent to this circle tangent this will be radius this will form 90 degree okay this is a fun Dyer right now so how to find is lengthen of PQ so this this I know this is radius okay this is the radius so dis Lenzi so much this length is three this length is 3 how many is this length down so this whole is 12 - 12 - these three 9 and - this 300 right there - these threes is also three now because this the radius is 3 okay so this is the radius is 3 this radius is 3 this is also 3 so that is also 3 right so 12 minus 3 plus 3 that is 6 it becomes 6 so this is 6 this is 3 so what is P Q so now P Q is equal to P Q is equal to 203 square plus 6 square that is root 45 that is 3 root 5 3 root 5 so again a very good question fine okay let's move to net problem now see each question in a right angle triangle in a right angled triangle area is given as 80 square units and parameter is also given as 80 units 80 units right so both are given so we need to find the find the find the length of hypotenuse right it may be a tricky question right this easy question but it can be a tricky question if you don't use this funda that in radius of any right angle triangle is what semi-perimeter - hypotenuse okay and second one was what area is equal to R into S okay now a label to our interest areas even as gaetti are I need to I can calculate here and s is given as word what is s SS same perimeter so half of it is what 14 therefore you get R is equal to 2 so if you get are able to different places are 2 here so R is 2 for the same perimeter 40 okay so it is hypotenuse so I put 10 use becomes 138 so 38 is the answer for this question right so the good question right fit on just BC Fonda that's it okay next question this question is what is the area of the triangle what is the area of the triangle with circumradius 8 so not circle medicine which circumradius it D is circumradius 18 and in radius is equal to 8 here's a question right what is the area of triangle with circumradius ability teen and in a radius 8 ok let's solve it now now we know that in here adding in triangle what is circumradius it's circumradius is 18 and it is what it is 1/2 of the hypotenuse so I can get the hypotenuse is what so hypotenuse length is 136 okay so length of hypotenuse is 136 okay now if length of hypotenuse is 36 and here is small R is again 8 so again same in a radius is what semi-perimeter - hypotenuse now 8 is equal to same perimeter - hypotenuse 36 that means semi-perimeter becomes what it becomes 44 therefore what is a perimeter perimeter is what perimeter is 88 so perimeter is 88 right so if a beta is 88 so what is the area there for area of any triangle is what given as what R into S so R is what here R is 8 and SS 44 what is answer 14 to 8 is 324 into 8 32 so 3 20% a - 350 - so answer for this question is what 350 to this answer okay for the area of triangle with R equal to 18 and R equal to that is circumcenter capital or capital R is what circumcenter what is smaller in its step tears or circumcenter circumradius and what is smaller in red is red okay next question we'll do right now the right angle triangle in a right angle triangle ABC are its sides are its sides such that C is greater than B is greater than a right that is given that it is given that 2a plus 7c equal to 9 B this is given and a is equal to 12 business of given right so find the length of C find the value of C okay now it's a very good question right if you get don't read any concept it very tough question it will keep on solving they spend you spend five minutes on it you will not get the answer right you saw the correct away he will get the answer right so you know that ABC has a sides of the triangle okay and a is greater than B is written and C that means C is the hypotenuse E is the smaller side that is 12 is also given right okay so now what we can do here is in this case you can write like this C to a plus 7c equal to seven B plus to be fine that means 2 into a minus B is equal to 7 into B minus C that means a minus B upon B minus C is equal to 7 by 2 now very important equation right so if a minus B upon B minus C is equal to n by 2 then I just need to find a side I know that ABC is in a triplet ABC is any triplet right here I just need to find a triplet here just need to find it the criteria which difference of a and B is 7 right a väsby 7 and difference of B and C is to this I need to find it right so if you observe all those basic triplets which I told to you truly to remember three four five five twelve thirteen seven twenty four twenty five eight fifteen seventeen right nine forty forty one like this will write all the triplet 2229 so you see that eight fifteen seventy satisfies it right difference between a and B is seven that is eight and fifteen eight and fifteen difference is seven and B and C differences to decided to satisfy this right that means eight to fifteen so ABC 8:15 17:3 blip satisfies it's a very good question right which talks about the understanding of the triplets right if you know the triplets into it very fast right otherwise they put the value of equal to well to serve it in trial go to tballga bruh i did not really upset way difficult right lending huh so now you know that now it is even that e is equal to a naught is given that eager tool right so what I can do is also I can put the value of a to L where but simply it is like ABC is a to 1517 triplet right now since a equal to 2 a 12 so instead of 8 8 is 12 right that means this triplet is what this triplet is 1.5 times the ordinal into 1.5 is multiplication right in to 1.5 the script that is what 1.5 times the original okay so if 8 is if 8 is 12 then I need to value value of C it C is the hypotenuse because given that a is less than B & B is less than C you see is the longest side C is the hypotenuse so if 8 is 12 that node is 17 again 1.5 times so into 1.5 25.5 that is therefore C becomes 25.5 right very good question super question okay see is what 25.5 okay now in this video we'll discuss further concept thank you [Music]