In the following figure, O is the center of the circle. Find the value of c.

We know that,

Angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference.

∠AOB = 2∠ACB = 2 x 50° = 100°.

Also, OA = OB = radius of circle.

∴ ∠OBA = ∠OAB = c [As angles opposite to equal sides are equal]

In △OAB,

⇒ ∠OAB + ∠AOB + ∠OBA = 180°

⇒ 2∠OAB + 100° = 180° [∵ ∠OBA = ∠OAB and ∠AOB = 100°]

⇒ 2c + 100° = 180°

⇒ 2c = 180° - 100°

⇒ 2c = 80°

⇒ c = $\dfrac{80}{2}$ = 40°.

Hence, c = 40°.