Question

In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm, Calculate the radius of the circle.

• A. 12.25 cm
• B. 21.10 cm
• C. 11.25 cm
• D. 13.95 cm

Answer 1

The correct option is C

11.25 cm

$\angle OBA={90}^{\circ }$

(Radius throught the point of contact is perpendicular to the tangent)

$\Rightarrow O{B}^2=O{A}^2-A{B}^2$ [By Pythagoras Theorem]
$\Rightarrow r^2=(r+7.5{)}^2-{15}^2$

$\Rightarrow r^2=r^2+56.25+15r-225$

$\Rightarrow 15r=168.75$
$\Rightarrow r=\frac{168.75}{15}$$\Rightarrow r=11.25$

Hence, radius of the circle =11.25 cm