Question

In following fig., PT is tangent to the circle at T and CD is a diameter of the same circle. If PC= 3cm and PT= 6cm, find the radius of the circle.

Answer 1

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

Since, PCD is a secant and PT is a tangent to the given circle, we have

PC · PD = PT² 

3 . (3 +2x) = 6² 

⇒ 9 + 6x = 36 

⇒ 6x = 27   

⇒ x = `27/6 = 9/2`

Radius of the circle is `9/2` cm , diameter is 9 cm