Question

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q, so that $OQ=12$ cm. Length of PQ is :

• A. $\sqrt{112}$ cm
• B. $\sqrt{113}$ cm
• C. $\sqrt{85}$ cm
• D. $\sqrt{119}$ cm

Answer 1

The correct option is D $\sqrt{119}$ cm

Given,

Radius OP=$5$cm and OQ=$12$cm

PQ is the tangent to the circle.

$\angle OPQ={90}^0$

So,by Pythagoras theorem we get,

$P{Q}^2=O{Q}^2-O{P}^2$

$=>P{Q}^2={12}^2-5^2$

$=>P{Q}^2=144-25$

$=>P{Q}^2=119$

$=>PQ=\sqrt{119}$cm