Question

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

Answer 1

Given, PA and PB are the tangents to a circle with center O and CD is a tangent at E and PA = 14 cm.
Tangents drawn from an external point are equal.
∴ PA = PB, CA = CE and DB = DE
Perimeter of  Δ PCD = PC + CD + PD
= (PA- CA)+( CE +DE) +( PB- DB)
= (PA -CE)+ (CE+ DE)+( PB- DE)
=(PA+ PB)
= 2PA(∵ PA= PB)

=(2×14) cm

= 28 cm

=28 cm
∴ Perimeter of ΔPCD = 28cm.