Question

PQ and PR are tangents in the given figure. Find PQ (in cm).

• A. 12
• B. 14
• C. 10
• D. 8

Answer 1

The correct option is D

8

OS = OQ = radius = 6 cm

$\angle PQO={90}^{\circ }$
(Tangent PQ is perpendicular to radius QO at point of contact Q.)

$△$ PQO is right angled at $\angle PQO$ and PO is hypotenuse as it is side opposite right angle PQO.

By Pythagoras theorem, the square of hypotenuse is equal to sum of squares of other 2 sides.

Thus,
${PO}^2$ = ${PQ}^2$ + ${OQ}^2$

So,
${10}^2$ = ${PQ}^2$ + $6^2$

${PO}^2$ = ${10}^2$ - $6^2$

${PQ}^2$ = 64

$\Rightarrow PQ=8cm$