Q. 15 C

# Three points A, B and C lie on the circle with centre O in such a way that AOCB is a parallelogram, let us calculate the value of ∠AOC.

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°

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