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Question

In figure ABCD is a cyclic quadrilateral; O is the centre of the circle. If BOD=160, find the measure of BPD , as shown in the given figure.

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Solution

Consider the arc BCD of the circle. This arc makes angle BOD=160 at the centre of the circle and BAD at a point A on the circumference.
BAD=12BOD=80
Now, ABCD is a cyclic quadrilateral.
BAD+BCD=180
80+BCD=180
BCD=100
BPD=BCD [BPD and BCD are angles in the same segment]
BPD=100

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