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 $\Delta$ PCD.

Answer 1

Here is the answer to your query.

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

We know that lengths of lengths drawn from as extend point to a circle are equal

∴ PA = PB = 14 cm

CA = CE

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