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 ΔPCD.

In the given fig.,

CA and CE are the two tangents drawn from an external point C at the point of contacts A and E respectively.

∴ CA = CE

[∵ Tangents drawn from an exterior point to the circle are equal in length]

Similarly, DE and DB are the two tangents drawn from an external point D at the point of contacts E and B respectively.

∴ DE = DB

[∵ Tangents drawn from an exterior point to the circle are equal in length]

Perimeter of Δ PCD = PC + CD + PD

= PC + CE + DE + PD

= PC + CA + BD + PD

= PA + PB [∵ PA = PC + CA and PB = PD + BD]

= 14 + 14 [∵ PA=PB]

= 28 cm