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Question

In the given figure, $$APB$$ is tangent at $$P$$ to the circle with the centre $$O$$. If $$\angle QPB={ 60 }^{ o }$$ then measure of $$\angle POQ=$$
611089.PNG


A
60o
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B
30o
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C
120o
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D
90o
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Solution

The correct option is B $${120}^{o}$$
Given that:
$$\angle QPB=60^\circ$$
To find:
$$\angle POQ=?$$
Solution:
$$\angle QPB=\angle QRP=60^\circ$$   (Alternate segment theorem)
$$\angle POQ=2\angle QRP=2\times60^\circ=120^\circ$$  (Angle subtended by the chord at the centre is twice of angle subtended by it at circumference.)
Hence, C is the correct option.

Maths

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