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 a circle.

Answer 1

Let OD = OC = x cm (radius of same circle)

Since ACD is a secant and AB is a tangent to the given circle, we have,

AC . AD = AB²

(7.5)(7.5 + 2x) = 15²

⇒ 56.25 + 15x = 225

⇒ 15x = 168.75 ⇒ x = 11.25

Thus, the radius of the circle is 11.25 cm.