Question

In the figure below, ABC is a triangle, AC and BC are tangents to the circle of center O at two different points. The lengths of AM, AR and BC are equal to 6 cm, 12 cm and 18 cm respectively. Find the radius of the circle.

Answer 1

AM$\times$ AB = $A{R}^2$

$\Rightarrow$6$\times$(6 +2r) = (12$\times$12)

$\Rightarrow$2r + 6 = 24

$\Rightarrow$ r = 9 cm