Q15 of 22 Page 126

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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