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.
11.25 cm
Let the radius of the circle be ‘r’ CD = 2r (given, CD is diameter of the circle) AB is tangent to the circle (given)
∴AB2=AC×AD
(15)2=7.5(7.5+2r)
15×15=7510(7.5+2r)
15×15=7510(7.5+2r)
30=7.5+2r
22.5=2r
r=11.25 cm