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Question

In the given figure, if tangents PA and PB from a point P to circle with centre O are inclined to each other at an angle of $$72^{\circ}$$ then measure of $$\angle POA$$ is :

83643_bdc3fafe2c8c40259d5ea87dde59ed1c.png


A
36
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B
90
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C
54
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D
72
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Solution

The correct option is A $$54^{\circ}$$
$$OA = OB$$ radii of the same circle
$$PA = PB$$ tangents drawn from the same external point are equal in length
So triangles $$OAP$$ and $$OBP$$ are congruent.
$$\Rightarrow \angle OPA = \angle OPB = \dfrac{72^o}{2} = 36^o$$.
Tangent and radius are perpendicular at the point of contact, so $$\angle OAP = 90^o$$.
Therefore, $$\angle POA = 90 - 36 = 54^o$$.
So option C is the right answer.

Mathematics

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