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. ${36}^{\circ }$
• B. ${90}^{\circ }$
• C. ${54}^{\circ }$
• D. ${72}^{\circ }$

Answer 1

Answer: (C)

${54}^{\circ }$

$OA=OB$ 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.

$\Rightarrow \angle OPA=\angle OPB=\frac{{72}^o}{2}={36}^o$.

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.