Geometric Shapes: Special Triangles

[Music] [Music] hi everyone my name is Ray Prakash and this is the 14th class of geometric right geometry 14 and this will discuss about a 30-60-90 triangles 30-60-90 triangles it's applications 45-45-90 triangles its application than equilateral triangle and all right so we'll discuss it okay see 30-60-90 triangle 30-60-90 triangle now what is this 30-60-90 triangle ready in name you can see it contains a 90 degree that means it is for right angle triangle it is for right angle triangle right now similarly 45 45 45 45 45 90 triangle trade again it's for writing it there's two kinds of writing a triangle right two kinds of right angle triangle most frequently used so 90 it says this is 30 this is become 60 in 45 45 90 let's say this is 90 this is 45 this becomes 40 right so this is quite easy 45 45 90 triangle because it is right-angled Isis a love triangle in any triangle if two angles are equal then opposite sides are also equal so this it's 45 45 so these two sides are also equal right so if 45 is opposite I assume it to be one this also becomes 1 so this becomes 2 the ratio ratio is 1 h21 h21 h21 is 2 root right ratio is 1 is to 1 is 2 root 2 by PI theorem it comes becomes root 2 right now in 30 60 90 90 triangle we need to derive it right so let's assume 30 opposite to be 1 it's a zone 30 opposite to be 1 right now applying pants HD here applying pants 60 here just on safety and 60 his word perpendicular by base so what is tan 68 is root three perpendicular is what whichever side angle you're taking opposite is perpendicular this is P so B and what is a base this lift this is base rate this one because this is hypotenuse so whichever angle you are taking its opposite is perpendicular one is for sure hypotenuse the left out left out one is the base right all this so he can watch this basics of trigonometry video going by me have recorded it right so please watch this video so tan 60 is root 3 root trees P upon B is 1 bi has zoomed to one right therefore P is now root 3 so if P is root 3 then what I can do okay P becomes root 3 then H is what 201 is square plus root 3 square right that means H becomes root 4 that is 2 right so H becomes root H becomes 2 so if 30 opposite I assume to be working to be 160 opposite is root 3 and 90 a positive 2 so the ratio it becomes 1 a 2 root 3 H 2 to 1 H 2 root 3 is to 2 so 30-60-90 the ratio is 1 is 2 root 3 to do 30 above it is 160 about is root 3 94 interval a positive to 45-45-90 what is the ratio 1 into root C it's the application right we'll see its application ok remember it just remember it 30-60-90 ratio is 1 H 2 root 3 is to 2 ok and 45-45-90 ratio is 1 a 2 1 a 2 2 root 30 60 90 45 45 90 okay now now see see you in right angle so no take radical I get any angle wrong we see its application okay see any triangle it's a super angle and if triangle has this triangle is ABC and this is the altitude this is 90 degree okay this ad and this lens is let's say hundred okay this is 60 degree sorry make it 30 degree this is 30 degree and this is 45 days right now see it's a similar application you can see in height and distance chapter in telemetry right some let's say this is a building ad there is a building ad here right here's a building ad on one side and this is the this is the earth this is a building this is a one building or 500 meter if I see from one side the angle if I see it from point A right or point B I can write point B the angle of elevation is 30 degree this is the angle of elevation right angle evolution is seen upward okay and if I see if I see it from Point C the angle of elevation becomes 45 degree so see the angle of elevation red sync up notice angle of depression so angle of elevation or angle of depression it is always formed by the horizontal line and will of elevation or depression and depression right always formed by the horizontal line right suppose if you if I ask you okay from this point from this point angle of depression to point B this is point B right is this point to B so if I ask you the angle of depression from point A angel' of depression to point B is 30 degree so point a angle of depression so don't mark this angle 30 degree right no angle is always with horizontal line so draw a horizontal line here right and then this angle is 30 degree so angle of depression from point A to B this is 30 degree not this one not this one right so this is a similar application to hide in distance chapter fine okay this ad is 100 now so see ya in this triangle now 30 a poet is hundred if 30 opposite is 100 then 90 so we see this ratio this is 30 this is 90 so this automatically becomes 60 this automatically becomes 60 this is for 90 s it is 45 so this becomes 45 now see this triangle this is the 30-60-90 triangle right so in 30-60-90 triangle what is the ratio ratio is 1 h 2 root 3 it to 2 if 30 ippolit is 1 then 90 a pod is to double so if 30 ipod is 100 so 90 ipod is what 200 right so I I draw a figure with a weak see triangle ad as the Alta tool and ad is given as hundred so with this information I can find each and every length in this figure that's what I'm showing you right so 30 point is 190 Papa's it is 200 what is the ratio what I should do now third D a boy it is 160 a boy it is root 3 so 30 a boy it is 100 put acidity opposite 100 root 3 what is the ratio 1 is 2 root 3 so 60 abode is 100 okay fine in this case here 45 opposite is 1 so 45 of a poet is 1 so it is also 1 it is root 2 here 45 point is hundred this also becomes hundred and this becomes so one is to ensure root 2 so one hundred one hundred and hundred root right so the good we got to answer it with this information I have calculated every method figure in this every other length in this figure this is the application of 30-60-90 triangle and 45-45-90 triangle okay now see we'll keep on using it down right now I will keep I'll use it in case of equilateral triangle right equilateral triangle we'll discuss all the concepts about equilateral triangle right and we'd apply 30-60-90 concept also see equilateral triangles what an equilateral triangle first of all in equilateral triangle first of all all sides are equal that we know obviously all angles are equal and they're equal to how much 60 degree okay in center circumcenter centroid and orthocenter are same point are same point in equilateral triangle are same point in equilateral triangle 8 so all sides are equal all angles are equal to 60 degree in center circumcenter centroid and orthocenter all are same point in equilateral triangle ok so see in this case in this case you're drawing equilateral triangle here see equilateral triangle ABC all sites let's say a eight and hey all are equal right now if I drop a perpendicular here right if I drop a perpendicular here right now this perpendicular since also centered lies on perpendicular so let's say orthocenter V lies somewhere here right now also Center is equal to centroid that means this ad is VD n as well right let me write like this this ad this whole is obviously right this whole is a so since also centralized on perpendicular so this is like Occident also centered and also center and centroid at same point so this is centroid also that means ad is median also right that means ad is altitude ad is also median right so he D is median also okay now if ad is median here that means centroid divides median in the ratio of 2 is to 1 that means this is the ratio of 2 ish-200 centroid divides median in the ratio of 2 is to 1 okay now LD is this circle this point let's at this point oh this point O is the circumcenter as well as in center circle Center means keeping this point as Center and taking any one vertex as radius taking any one vertex as radius right I can draw a circle which will touch triangle from outside right let me draw little bit a circle okay so which will touch triangle from outside like this something like this so this is the radius right and what is in radius so this in radius is keeping this as this keeping this as keeping any one side as perpendicular distance this is in radius I can draw a circle which will touch triangle from inside like this side is at Virginia this is in circle right so you can see here capital is here too small our here is one because it is centroid and centroid divides midden in the ratio of 2 is to 1 that means circumradius h2 in radius the ratio is what it is - H - 1 in case of equilateral triangle circumradius twopenny radius what is the ratio to which to 1 in case of equilateral triangles get this points in mind right you get this points in mind can draw and draw an email in mind right equilateral triangle all its full symmetrical figured ride also centered circumcenter in sentence centroid or line or a same point right that's why ad is median as well as gate is altitude as well as ad is the what you call angle bisector as well as KD is the side bisector all KD will be already all are same in case of ad right that means so for dotted perpendicular so all points are concurrent all are same point only that means there's one will be inside circle one will be outside circle since the Rishi says since it is centroid what is the ratio - ish - one so circumradius and innate is what is the ratio two to one in case of equilateral Frank okay now now let me write here again let me take equilateral triangle here so discussed all this point say it is all this point will be same now so ABC and now if I draw a perpendicular D here so this t-shirt is a median as well so it becomes a by two it becomes a by two this is angle bisector as well so all angles are 60 60 this becomes 30 and 30 right this is the this is the height of equilateral triangle right this is a this is C now you see triangle ADC triangle ABC is a 30-60-90 triangle right 30 60 negative angle here 30 opposite is a by 2 right so the ratio 30 60 90 ratio is 1 is 2 root 3 to 2 okay so 30 apposite is a by 2 so 60 fold is what a by root so what is the ratio 1 is to root 3 so 30 upward is a by do what is 60 apposite a by 2 root 3 that means height of first point first point height of equilateral triangle is a by 2 root 3 this is the first point in case of equilateral number it the first point in case of equal equilateral triangle height is a by 2 root 3 second point area what is the area of it equilateral triangle what is the area area is half into height into base right what is the area half into what is the height a by 2 root 3 what is the base this whole base is this whole is the base that is a right so half into T right therefore therefore area becomes root 3 by 4 into a square second important point area is root 3 by 4 a square first point height is a by 2 root 3 how it comes it comes simply by 30 section at the application so a day is root 3 by 4 into ka square okay third point Third Point C third point is circumradius and unit is rate so we just discussed we just discussed right now that this point is circumcenter as well as in center this ratio will you or disraeli 2h 2 1 right this ratio is what 2 is to 1 that is 1 is in radius this 2 with circumradius capital r right so this obviously this R plus R is the height this R plus R is the height of the equilateral triangle and his height is divided in the ratio of 2 which to 1 that means that means circumradius is what it is 2 by 3 of height right that means 2 by 3 into it is height D by 2 root 3 so you get cancel it to 2 it becomes a by root 3 another super important point circumradius word circumradius is a by root 3 in an equilateral triangle and since in radius as half of it so what is in radius K by 2 3 in radius escape I'd say right R is capital capital R is 2 smaller is 1 so any radius is half of circumradius so what is in radius ay by 2 root 3 and also get in radius by what is in radius here it is 3 1 by 3 of height ratio to each to 1 so in it is what 1 by T of hydrate you get any reduces a by 2 root 3 so 3rd and 4th so for first second third and fourth right for super important points in case of equilateral triangle should remember it capital R a by root 3 is smaller a by 2 root 3 height is area is root 3 by 4 a square and height is odd K by 2 root 3 this is the height of equilateral triangle ok now let's do a question you question this is a equilateral triangle there is if there is a equilateral triangle which side which side two units right a circle is circumscribing it a circle is circum describing it and another circle is inscribing it in describing it correct now to the outer circle to the outer circle again again an equilateral triangle is drawn again an equilateral triangle is drawn which which any scribes the witch in his cries the outer circle which is Christ the chorus should right sorry which again and equal tangent drawn to which - which - which outer circle acts as in circle okay so find thee find the area of the bigger equilateral triangle right so straight a question here the question is real language problem right nothing else oh she says there is an equilateral triangle right there is a circle which inscribe set your circle which circumscribe set like this right and then again there's a collateral triangle to which outer circle acts as in circle right that means this is again an equilateral triangle drawn like this right I have drawn best possible diagram played kindly cooperate so now for this equilateral triangle this side is given as two units this side is given as two units we're finding the side of the outer side what is side of the outer prime the right it's very easy cut and ready observe it here see in this equilateral triangle this centre is a common right this centre is the common okay for both this circle for both this circle this is a common centre right so if an equilateral if here the equilateral triangle has side too okay so you can see it yeah it's if an equilateral triangle has side - you can say it for the circumradius right for this triangle is circumradius circumradius circum it is alright circumradius are put is our R is a by root 3 right this this is 2 is given as 2 circumradius sorry now two side is given as 230 circumradius circumradius what 2 by root 3 for this equilateral triangle this circumradius right is circumradius becomes word it becomes 2 by root 3 fine 2 by root 3 now again in this bigger for this bigger triangle for this bigger triangle this circle access this circle access in circle so if this side if this side of the bigger triangle it say it is not mentioned here that would mention K make some other side here right let's the side is X so circumradius a by root three general formula a here is given as to a here is given as 2 so it circumradius becomes 2 by root 3 ok now to this bigger to this bigger circle is the in circle for outer triangle so if the outer triangle has side X its inner radius should be how much X by 2 3 right this inner radius of outer set you should be how much this is the unit is right this for this circle it is X by 2 root 3 and this is the this is the circumradius for thee this is a circumradius for the inner circle right this same radius is given by 2 2 by root 3 so I can equate it then for 2 by root 3 is equal to X by 2 root 3 right this roots roots they cancel so X becomes 4 that's the answer it X becomes 4 therefore X becomes 4 so 4 is the answer what is the area areas what area is root 3 by 4 a square if X is 4 so area becomes area becomes so 3 by 4 into side is quelled at his Foursquare this is the answer right this is the answer so again come back to it what is the question question was there's an equilateral triangle a circle is in ascribing it as it a circle is circumscribing it this circle this triangle right now there is again an equilateral triangle drawn which to which the outer circle acts as the in circle right so again an equal at a tangled on this bigger one to which this outer circle acts as the in circle tactic in circle right so if outer circle has side oh sorry if outer triangle aside X so this is the in circle for it so it is the inner radius this inner radius is what this inner it is nothing but this is the inner radius for the outer circle or triangle right what is the in radius X by 2 3 or just restricted previous slide so it is in radius X by 2 3 right and when equating and when staying from the inner triangle for inner triangle exact it access this circle access circumradius so if in a triangle has sided to what a circle it is 2 by root 3 so both a circle has a radius same we can equate it this root 3 root 3 cancels X equal to 4 so if s equal to 4 what is the area of either triangle whose 3 by 4 into 4 is 4 ok so it's a good question very good question good concept right how do you note it ok so study further in each video thank you [Music]

[Music] [Music] hi everyone my name is Ray Prakash and this is the 14th class of geometric right geometry 14 and this will discuss about a 30-60-90 triangles 30-60-90 triangles it&#39;s applications 45-45-90 triangles its application than equilateral triangle and all right so we&#39;ll discuss it okay see 30-60-90 triangle 30-60-90 triangle now what is this 30-60-90 triangle ready in name you can see it contains a 90 degree that means it is for right angle triangle it is for right angle triangle right now similarly 45 45 45 45 45 90 triangle trade again it&#39;s for writing it there&#39;s two kinds of writing a triangle right two kinds of right angle triangle most frequently used so 90 it says this is 30 this is become 60 in 45 45 90 let&#39;s say this is 90 this is 45 this becomes 40 right so this is quite easy 45 45 90 triangle because it is right-angled Isis a love triangle in any triangle if two angles are equal then opposite sides are also equal so this it&#39;s 45 45 so these two sides are also equal right so if 45 is opposite I assume it to be one this also becomes 1 so this becomes 2 the ratio ratio is 1 h21 h21 h21 is 2 root right ratio is 1 is to 1 is 2 root 2 by PI theorem it comes becomes root 2 right now in 30 60 90 90 triangle we need to derive it right so let&#39;s assume 30 opposite to be 1 it&#39;s a zone 30 opposite to be 1 right now applying pants HD here applying pants 60 here just on safety and 60 his word perpendicular by base so what is tan 68 is root three perpendicular is what whichever side angle you&#39;re taking opposite is perpendicular this is P so B and what is a base this lift this is base rate this one because this is hypotenuse so whichever angle you are taking its opposite is perpendicular one is for sure hypotenuse the left out left out one is the base right all this so he can watch this basics of trigonometry video going by me have recorded it right so please watch this video so tan 60 is root 3 root trees P upon B is 1 bi has zoomed to one right therefore P is now root 3 so if P is root 3 then what I can do okay P becomes root 3 then H is what 201 is square plus root 3 square right that means H becomes root 4 that is 2 right so H becomes root H becomes 2 so if 30 opposite I assume to be working to be 160 opposite is root 3 and 90 a positive 2 so the ratio it becomes 1 a 2 root 3 H 2 to 1 H 2 root 3 is to 2 so 30-60-90 the ratio is 1 is 2 root 3 to do 30 above it is 160 about is root 3 94 interval a positive to 45-45-90 what is the ratio 1 into root C it&#39;s the application right we&#39;ll see its application ok remember it just remember it 30-60-90 ratio is 1 H 2 root 3 is to 2 ok and 45-45-90 ratio is 1 a 2 1 a 2 2 root 30 60 90 45 45 90 okay now now see see you in right angle so no take radical I get any angle wrong we see its application okay see any triangle it&#39;s a super angle and if triangle has this triangle is ABC and this is the altitude this is 90 degree okay this ad and this lens is let&#39;s say hundred okay this is 60 degree sorry make it 30 degree this is 30 degree and this is 45 days right now see it&#39;s a similar application you can see in height and distance chapter in telemetry right some let&#39;s say this is a building ad there is a building ad here right here&#39;s a building ad on one side and this is the this is the earth this is a building this is a one building or 500 meter if I see from one side the angle if I see it from point A right or point B I can write point B the angle of elevation is 30 degree this is the angle of elevation right angle evolution is seen upward okay and if I see if I see it from Point C the angle of elevation becomes 45 degree so see the angle of elevation red sync up notice angle of depression so angle of elevation or angle of depression it is always formed by the horizontal line and will of elevation or depression and depression right always formed by the horizontal line right suppose if you if I ask you okay from this point from this point angle of depression to point B this is point B right is this point to B so if I ask you the angle of depression from point A angel&#39; of depression to point B is 30 degree so point a angle of depression so don&#39;t mark this angle 30 degree right no angle is always with horizontal line so draw a horizontal line here right and then this angle is 30 degree so angle of depression from point A to B this is 30 degree not this one not this one right so this is a similar application to hide in distance chapter fine okay this ad is 100 now so see ya in this triangle now 30 a poet is hundred if 30 opposite is 100 then 90 so we see this ratio this is 30 this is 90 so this automatically becomes 60 this automatically becomes 60 this is for 90 s it is 45 so this becomes 45 now see this triangle this is the 30-60-90 triangle right so in 30-60-90 triangle what is the ratio ratio is 1 h 2 root 3 it to 2 if 30 ippolit is 1 then 90 a pod is to double so if 30 ipod is 100 so 90 ipod is what 200 right so I I draw a figure with a weak see triangle ad as the Alta tool and ad is given as hundred so with this information I can find each and every length in this figure that&#39;s what I&#39;m showing you right so 30 point is 190 Papa&#39;s it is 200 what is the ratio what I should do now third D a boy it is 160 a boy it is root 3 so 30 a boy it is 100 put acidity opposite 100 root 3 what is the ratio 1 is 2 root 3 so 60 abode is 100 okay fine in this case here 45 opposite is 1 so 45 of a poet is 1 so it is also 1 it is root 2 here 45 point is hundred this also becomes hundred and this becomes so one is to ensure root 2 so one hundred one hundred and hundred root right so the good we got to answer it with this information I have calculated every method figure in this every other length in this figure this is the application of 30-60-90 triangle and 45-45-90 triangle okay now see we&#39;ll keep on using it down right now I will keep I&#39;ll use it in case of equilateral triangle right equilateral triangle we&#39;ll discuss all the concepts about equilateral triangle right and we&#39;d apply 30-60-90 concept also see equilateral triangles what an equilateral triangle first of all in equilateral triangle first of all all sides are equal that we know obviously all angles are equal and they&#39;re equal to how much 60 degree okay in center circumcenter centroid and orthocenter are same point are same point in equilateral triangle are same point in equilateral triangle 8 so all sides are equal all angles are equal to 60 degree in center circumcenter centroid and orthocenter all are same point in equilateral triangle ok so see in this case in this case you&#39;re drawing equilateral triangle here see equilateral triangle ABC all sites let&#39;s say a eight and hey all are equal right now if I drop a perpendicular here right if I drop a perpendicular here right now this perpendicular since also centered lies on perpendicular so let&#39;s say orthocenter V lies somewhere here right now also Center is equal to centroid that means this ad is VD n as well right let me write like this this ad this whole is obviously right this whole is a so since also centralized on perpendicular so this is like Occident also centered and also center and centroid at same point so this is centroid also that means ad is median also right that means ad is altitude ad is also median right so he D is median also okay now if ad is median here that means centroid divides median in the ratio of 2 is to 1 that means this is the ratio of 2 ish-200 centroid divides median in the ratio of 2 is to 1 okay now LD is this circle this point let&#39;s at this point oh this point O is the circumcenter as well as in center circle Center means keeping this point as Center and taking any one vertex as radius taking any one vertex as radius right I can draw a circle which will touch triangle from outside right let me draw little bit a circle okay so which will touch triangle from outside like this something like this so this is the radius right and what is in radius so this in radius is keeping this as this keeping this as keeping any one side as perpendicular distance this is in radius I can draw a circle which will touch triangle from inside like this side is at Virginia this is in circle right so you can see here capital is here too small our here is one because it is centroid and centroid divides midden in the ratio of 2 is to 1 that means circumradius h2 in radius the ratio is what it is - H - 1 in case of equilateral triangle circumradius twopenny radius what is the ratio to which to 1 in case of equilateral triangles get this points in mind right you get this points in mind can draw and draw an email in mind right equilateral triangle all its full symmetrical figured ride also centered circumcenter in sentence centroid or line or a same point right that&#39;s why ad is median as well as gate is altitude as well as ad is the what you call angle bisector as well as KD is the side bisector all KD will be already all are same in case of ad right that means so for dotted perpendicular so all points are concurrent all are same point only that means there&#39;s one will be inside circle one will be outside circle since the Rishi says since it is centroid what is the ratio - ish - one so circumradius and innate is what is the ratio two to one in case of equilateral Frank okay now now let me write here again let me take equilateral triangle here so discussed all this point say it is all this point will be same now so ABC and now if I draw a perpendicular D here so this t-shirt is a median as well so it becomes a by two it becomes a by two this is angle bisector as well so all angles are 60 60 this becomes 30 and 30 right this is the this is the height of equilateral triangle right this is a this is C now you see triangle ADC triangle ABC is a 30-60-90 triangle right 30 60 negative angle here 30 opposite is a by 2 right so the ratio 30 60 90 ratio is 1 is 2 root 3 to 2 okay so 30 apposite is a by 2 so 60 fold is what a by root so what is the ratio 1 is to root 3 so 30 upward is a by do what is 60 apposite a by 2 root 3 that means height of first point first point height of equilateral triangle is a by 2 root 3 this is the first point in case of equilateral number it the first point in case of equal equilateral triangle height is a by 2 root 3 second point area what is the area of it equilateral triangle what is the area area is half into height into base right what is the area half into what is the height a by 2 root 3 what is the base this whole base is this whole is the base that is a right so half into T right therefore therefore area becomes root 3 by 4 into a square second important point area is root 3 by 4 a square first point height is a by 2 root 3 how it comes it comes simply by 30 section at the application so a day is root 3 by 4 into ka square okay third point Third Point C third point is circumradius and unit is rate so we just discussed we just discussed right now that this point is circumcenter as well as in center this ratio will you or disraeli 2h 2 1 right this ratio is what 2 is to 1 that is 1 is in radius this 2 with circumradius capital r right so this obviously this R plus R is the height this R plus R is the height of the equilateral triangle and his height is divided in the ratio of 2 which to 1 that means that means circumradius is what it is 2 by 3 of height right that means 2 by 3 into it is height D by 2 root 3 so you get cancel it to 2 it becomes a by root 3 another super important point circumradius word circumradius is a by root 3 in an equilateral triangle and since in radius as half of it so what is in radius K by 2 3 in radius escape I&#39;d say right R is capital capital R is 2 smaller is 1 so any radius is half of circumradius so what is in radius ay by 2 root 3 and also get in radius by what is in radius here it is 3 1 by 3 of height ratio to each to 1 so in it is what 1 by T of hydrate you get any reduces a by 2 root 3 so 3rd and 4th so for first second third and fourth right for super important points in case of equilateral triangle should remember it capital R a by root 3 is smaller a by 2 root 3 height is area is root 3 by 4 a square and height is odd K by 2 root 3 this is the height of equilateral triangle ok now let&#39;s do a question you question this is a equilateral triangle there is if there is a equilateral triangle which side which side two units right a circle is circumscribing it a circle is circum describing it and another circle is inscribing it in describing it correct now to the outer circle to the outer circle again again an equilateral triangle is drawn again an equilateral triangle is drawn which which any scribes the witch in his cries the outer circle which is Christ the chorus should right sorry which again and equal tangent drawn to which - which - which outer circle acts as in circle okay so find thee find the area of the bigger equilateral triangle right so straight a question here the question is real language problem right nothing else oh she says there is an equilateral triangle right there is a circle which inscribe set your circle which circumscribe set like this right and then again there&#39;s a collateral triangle to which outer circle acts as in circle right that means this is again an equilateral triangle drawn like this right I have drawn best possible diagram played kindly cooperate so now for this equilateral triangle this side is given as two units this side is given as two units we&#39;re finding the side of the outer side what is side of the outer prime the right it&#39;s very easy cut and ready observe it here see in this equilateral triangle this centre is a common right this centre is the common okay for both this circle for both this circle this is a common centre right so if an equilateral if here the equilateral triangle has side too okay so you can see it yeah it&#39;s if an equilateral triangle has side - you can say it for the circumradius right for this triangle is circumradius circumradius circum it is alright circumradius are put is our R is a by root 3 right this this is 2 is given as 2 circumradius sorry now two side is given as 230 circumradius circumradius what 2 by root 3 for this equilateral triangle this circumradius right is circumradius becomes word it becomes 2 by root 3 fine 2 by root 3 now again in this bigger for this bigger triangle for this bigger triangle this circle access this circle access in circle so if this side if this side of the bigger triangle it say it is not mentioned here that would mention K make some other side here right let&#39;s the side is X so circumradius a by root three general formula a here is given as to a here is given as 2 so it circumradius becomes 2 by root 3 ok now to this bigger to this bigger circle is the in circle for outer triangle so if the outer triangle has side X its inner radius should be how much X by 2 3 right this inner radius of outer set you should be how much this is the unit is right this for this circle it is X by 2 root 3 and this is the this is the circumradius for thee this is a circumradius for the inner circle right this same radius is given by 2 2 by root 3 so I can equate it then for 2 by root 3 is equal to X by 2 root 3 right this roots roots they cancel so X becomes 4 that&#39;s the answer it X becomes 4 therefore X becomes 4 so 4 is the answer what is the area areas what area is root 3 by 4 a square if X is 4 so area becomes area becomes so 3 by 4 into side is quelled at his Foursquare this is the answer right this is the answer so again come back to it what is the question question was there&#39;s an equilateral triangle a circle is in ascribing it as it a circle is circumscribing it this circle this triangle right now there is again an equilateral triangle drawn which to which the outer circle acts as the in circle right so again an equal at a tangled on this bigger one to which this outer circle acts as the in circle tactic in circle right so if outer circle has side oh sorry if outer triangle aside X so this is the in circle for it so it is the inner radius this inner radius is what this inner it is nothing but this is the inner radius for the outer circle or triangle right what is the in radius X by 2 3 or just restricted previous slide so it is in radius X by 2 3 right and when equating and when staying from the inner triangle for inner triangle exact it access this circle access circumradius so if in a triangle has sided to what a circle it is 2 by root 3 so both a circle has a radius same we can equate it this root 3 root 3 cancels X equal to 4 so if s equal to 4 what is the area of either triangle whose 3 by 4 into 4 is 4 ok so it&#39;s a good question very good question good concept right how do you note it ok so study further in each video thank you [Music]

Transcript for:Geometric Shapes: Special Triangles

Transcript for:
Geometric Shapes: Special Triangles