The given figure represents a circle with centre O and arc AB=arc AC What is the measure of angle - Maths - Circles

Question

The given figure represents a circle with centre O and arc AB=arc
AC What is the measure of angle OCB ​

If we use the anglesum property of trianlge ABC, we get the angle
OCB to be 35 degree However, if we use the theorem, angle subtended
by a chord at the centre is twice the angle subtended by it at any
point on the circumference and then use anglesum property of
triangle OBC, we get angle OCB to be 20 degree How is it possible?

Anuradha Sharma · Accepted Answer

By using theorem, angle subtended by a chord at the centre is twice
the angle subtended by it at any point on the circumference
∠BOC=2∠BAC∠BOC=140 degreeNow in triangle BOC, OB=OC=radiusSo ∠OBC=∠OCB=180-1402=20 degreeNow We know only about angle A and angle ABO so we cannot use angle sum property in triangle ABC