Question

A tangent PQ at a point P on a circle of radius 5 cm meets a line through the center O at a point Q such that OQ =13 cm. Find the length of PQ.

• A. 12 cm
• B. 13 cm
• C. 8.5 cm
• D. $\sqrt{119}$

Answer 1

The correct option is A

12 cm

Given that OP = 5 cm, OQ = 13 cm

Applying Pythagoras theorem to triangle OPQ

${OP}^2$ + ${QP}^2$ = ${OQ}^2$

$5^2$ + ${QP}^2$ = ${13}^2$

${QP}^2=169–25=144$

$QP=\sqrt{144}cm$

QP = 12 cm