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Question

Consider the cyclic quadrilateral ABCD. If O is the centre of the circle and BOD = 160, then find the measure of BPD.


A

100

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B

80

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C

90

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D

70

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Solution

The correct option is A

100



We know that the angle subtended by an arc at the centre of a circle is double the angle subtended by it on any remaining part of the circle.

BAD=BOD2=80

Consider the cyclic quadrilateral ABPD. Since the opposite angles are supplementary,

BAD+BPD=180

i.e., 80+BPD=180

BPD=100


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