Question

3) In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. If CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find AB and PT

Answer 1

Since chord CD and tangent at point T intersect each other at P,

∴PC×PD=PT ²

.....(1)

Since chord AB and tangent at point T intersect each other at P.

∴PA×PB=PT ²

....(2)

From (1) and (2), PC×PD=PA×PB....(3)

Given: CD=7.8 cm;PD=5 cm,PB=4 cm.

∴PA=PB+AB=4+AB,PC=PD+CD=5+7.8=12.8 cm.

Putting these values in eq. (3)

12.8×5=(4+AB)×4

⇒4+AB= 4÷12.8×5

⇒4+AB=16

⇒AB=12 cm.

Hence, AB=12 cm.