Question

Circle is inscribed in an equilateral triangle the perimeter of circle is 132 cm then find the perimeter of triangle

Answer 1

perimeter of circle is 132 =2πr =2*22/7*r  

r==132*7÷22÷2=21 cm

Recall that incentre of a circle is the point of intersection of the angular bisectors.

Given ABC is an equilateral triangle and AD = h be the altitude.

Hence these bisectors are also the altitudes and medians whose point of intersection divides the medians in the ratio 2 : 1

∠ADB = 90° and OD = (1/3) AD

That is r = (h/3)

Þ h = 3r = 3 × 21= 63 cm

Let each side of the triangle be a, then

Altitude of an equilateral triangle is (√3/2) times its side

That is h = (√3a/2)

Altitude (a)=2h/√3=[2*63√3]÷√3*√3  =42√3 cm

a=42√3 cm

We know that perimeter of an equilateral triangle = 3a

3a = 3 × 42√3

3a= 126√3  

3a=126*1.732  =  218.232cm      ans

= 42 × 1.73 = 72.66 cm