Q. 74.8( 18 Votes )

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 PCD.


Answer :

Given : From an external point P, two tangents, PA and PB are drawn to a circle with center O. At a point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. And PA = 14 cm


To Find : Perimeter of PCD


As we know that, Tangents drawn from an external point to a circle are equal.


So we have


AC = CE …[1] [Tangents from point C]


ED = DB …[2] [Tangents from point D]


Now Perimeter of Triangle PCD


= PC + CD + DP


= PC + CE + ED + DP


= PC + AC + DB + DP [From 1 and 2]


= PA + PB


Now,


PA = PB = 14 cm as tangents drawn from an external point to a circle are equal


So we have


Perimeter = PA + PB = 14 + 14 = 28 cm


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