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Question

In the figure, O is the centre of the circle. If BOD=160, find the values of x and y.

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Solution

In the figure, O is the centre of the circle. ABCD is a cyclic quadrilateral.

BOD=160

arc BAD subtends BOD at the centre and BCD on the other part of the circle.

BCD=12BOD

x=12×160=80

ABCD is a cyclic quadrilateral,

A+C=180y+x=180

y+80=180y=18080=100

x=80, y=100


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