Question

OAB IS an equilateral triangle .If O is the centre of circle find the measure of angle ACB

Answer 1

Here
Angle aob, oba, bao =60degree ( equilateral triangle)
And angle abc= 90° ( right angle)
So a angle acb = 180°- (90+60)
=180-150=30°

Answer 2

By theorem

=>The angle subtended by an arc at the center is doubled the angle subtended by it at any point on the remaining part of circle.

& angle of equilateral triangle is 60°.
So, following this

angleAOB=2angleACB

60°/2=angleACB

30°=angle ACB.