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 PQ is :

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

Answer 1

Answer: (D)

$\sqrt {119}$ cm

Answer 2

We know that $PQ^2 =144 - 25$ the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
∴ $OP ⊥ PQ$
By applying Pythagoras theorem in $\text {ΔOPQ}$,

∴ $OP^2 + PQ^2 = OQ^2$
$5^2 + PQ^2 =12^2$
$25 + PQ^2 =144$
$PQ^2 =144 - 25$
$PQ^2 =119$
$PQ = \sqrt {119}\ cm$

Hence, the correct option is (D): $\sqrt {119}\ cm$