Question

In th O is the centre of the circle and angle AOB = angle Boc= angle COA. Find the perimeter of the triangle ABC

Answer 1

∠AOB = ∠BOC = ∠COA = 120°  (as their sum is 360° )

Angle made by chord AB at O = Angle made by chord BC at O

                 = angle made by chord CA  at O

Hence, AB = BC = CA.                 So ΔABC is equilateral.

O is the circumcenter of equilateral ΔABC.   

AO = radius = 2√3 cm = 2/3 * altitude from A

       (O is also the centroid)

Altitude from A =   √3/2 * AB

So   2/3 * √3/2 * AB = 2√3 cm

                           AB = 6 cm

Hence the perimeter = 3 * 6 = 18 cm