Question

In the given figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with center O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is

• A. 10 cm
• B. 7.5 cm
• C. 2.5 cm
• D. 4 cm

Answer 1

The correct option is D 4 cm

Join $OA$.

Triangles $OPA$ and $OQA$ are congruent.

$\Rightarrow \angle PAO=\angle QAO={45}^o$

Tangent and radius are perpendicular at the point of contact.

$\angle OPA={90}^o$

$\Rightarrow \angle OAP=\angle AOP={45}^o$

$\Rightarrow OP=AP=4cm$

So the radius of the circle is 4 cm.

So option D is the right answer.