Question

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

Answer 1

Let the radius of the circle be $r$.

$\therefore OB=OC=r$ and $OA=AC+OC=(7.5+r)cm$

$△ABO$ is a right angled triangle (since $AB$ is a tangent). By Pythagoras theorem,

$O{A}^2=A{B}^2+O{B}^2$

$\Rightarrow (7.5+r{)}^2={15}^2+r^2$

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

$\Rightarrow 15r=225-56.25=168.75$

$\Rightarrow r=11.25cm$