Q. 314.7( 4 Votes )

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.


Answer :

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


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