Question

From an external point P, tangents PA and PB are drawn to a circle with, centre O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of ∆PCD.

Answer 1

In the given figure,

CD is a tangent at E and

PA = 14 cm.

Now,

PA and PB are tangents from P to the circle.

PA = PB ….(1)

CA and CE are tangents to the circle.

CA = CE ….(2)

Similarly, BD and DE are tangents to the circle.

DB = DE

Now, perimeter of ∆PCD = Sum of all the sides

= PC + CD + PD

= PC + (CE + ED) + PD

[Using (1) and (2)]

= (PC + CA) + (BD + PD)

= PA + PB

= 14 + 14

= 28

Therefore, perimeter of ∆PCD is 28 cm