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 the point E and PA = 14 cm, find the perimeter of ∆PCD.
Figure

Answer 1

Given : PA and PB are tangents to the circle with centre O.
CD is a tangent to the circle at E, which intersects PA and PB at C and D, respectively, and PA = 14 cm.

We know that tangents drawn from an external point to a circle are equal.
∴ PA = PB = 14 cm
CA = CE and DB = DE
Now, perimeter of ΔPCD = PC + CD + PD
= PC + (CE + ED) + PD
= PC + (CA + DB) + PD
= (PC + CA) + (DB + PD)
= PA + PB
= 14 cm + 14 cm = 28 cm