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Question

In figure, if O is the centre of a circle, PQ is a chord and the tangent PR makes an angle of 50 with PQ, then POQ is equal to:

A
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B
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C
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D
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Solution

The correct option is C
We know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
OPR=90
OPQ+QPR=90 [From figure]
OPQ=9050=40 [QPR=50]
Now, OP = OQ = Radius of circle
OQP=OPQ=40
[Since, angles opposite to equal sides are equal]
In OPQ,O+P+Q=180
[Since, angles opposite to equal sides are equal]
O=180(4040) [P=40=Q]
= 18080=100

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