Question

An isosceles triangle with its vertices on a circle is shown in this picture.

What is the perimeter of the circle?

Answer 1

The circumference (perimeter) of the circle is: 5\(pi\)cm

Answer 2

Consider the centre of circle as O and triangle as ABC

OC = Radius of circle = r 

OD = 4 – r

AD = 2 cm

AO = r

Therefore, in triangle AOD

(AO)² = (AD)² + (OD)²

r² = 22 + (4 – r)²

r² = 4 +16 – 8r + r²

8r = 20;

r = 20/8

= 5/2

= 2.5 cm

∴ Perimeter = 2π × r

= 2π × 2.5 cm 

= 5π cm