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 $$\angle POQ=$$

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

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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