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, find the radius of the circle.

Answer 1

Let the radius of the circle be ‘r’ CD = 2r (given, CD is diameter of the circle) AB is tangent to the circle (given)

$\therefore A{B}^2=AC\times AD$

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

$15\times 15=\frac{75}{10}(7.5+2r)$

$15\times 15=\frac{75}{10}(7.5+2r)$

$30=7.5+2r$

$22.5=2r$

$r=11.25cm$