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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 a point E and PA = 14 cm, find the perimeter of ∆PCD.

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Given,

PA and PB are the tangents drawn from a point P outside the circle with centre O.

CD is another tangents to the circle at point E which intersects PA and PB at C and D respectively.

PA = 14 cm

PA and PB are the tangents to the circle from P

So, PA = PB = 14 cm

Now, CA and CE are the tangents from C to the circle.

CA = CE ….(i)

Similarly, DB and DE are the tangents from D to the circle.

DB = DE ….(ii)

Now, perimeter of ∆PCD

= PC + PD + CD

= PC + PD + CE + DE

= PC + CE + PD + DE

= PC + CA + PD = DB {From (i) and (ii)}

= PA + PB

= 14 + 14

= 28 cm

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