Question

In the figure, tangents PA and PB are drawn to a circle with center O from an external point P. If CD is a tangent to the circle at E and AP = 25cm, find the perimeter of ∠PCD,

Answer 1

We know that the lengths of the two tangents from an exterior point to a circle are equal.

CA = CE, DB = DE and PA = PB Now,

the perimeter of = PC + CD + DP 

= PC + CE + ED + DP 

= PC + CA + DB + DP 

= PA + PB = 2PA(PB = PA) 

Thus, the perimeter of ∠PCD = 2 × 25 = 50cm