Question 3
From an external point P, two tangents , PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.

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Solution

Two tangents PA and PB are drawn to a circle with centre O from an external point P.

Perimeter of $△$ PCD = PC+CD+PD
= PC+CE+ED+PD
= PC+CA+DB+PD
=PA+PB
=2PA=2(10)
=20 cm
[ $∵$ CE=CA DE = DB PA = PB tangents from internal point to a circle are equal]

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