Question

A B C are three points on a circle with centre O such that AOBC is a parallelogram find the value of angle AOC

Answer 1

Answer:

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°