Question

Three point A,B,C lie in a circle with centre O in such a way that AOCB is a parallelogram. Find the value of angle AOC.​

Answer 1

Step-by-step explanation:

As OABC is a parallelogram, therefore, opposite angles will be equal.

⇒ ∠AOC = ∠ABC --------- (1)

Also, ABCD is a cyclic quadrilateral, therefore sum of opposite angles must be 180°

⇒ ∠ADC + ∠ABC = 180 ---------- (2)

By the theorem:-

The angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.

∠AOC = 2 ∠ADC -------- (3)

From (1), (2) and (3), we get,

⇒ ∠AOC = 120°