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