Question

The length of the tangent to a circle from a point outside the circle measures 12 cm. The distance of the point from the centre is 15 cm.
Find the radius of the circle.

• A. 10cm
• B. 8cm
• C. 9cm
• D. 12cm

Answer 1

The correct option is C

9cm

The length of the tangent is given as 12 cm.

The distance of the point from the centre of the circle is given as 15 cm.

The radius from the point of contact, the tangent and the line segment from the centre to the external point form a right angled triangle.

Let r be the radius of the circle.

So by Pythagoras theorem,

$P{R}^2+(r{)}^2=O{P}^2$

$(12{)}^2+(r{)}^2=(15{)}^2$

$r^2=225-144=81$
$r=9$

Hence, the radius is 9 cm.