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 :

A
36
B
90
C
54
D
72

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 lengthSo 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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