Q. 335.0( 2 Votes )

In the given figure, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the perimeter of ΔEDF is


A. 9 cm

B. 12 cm

C. 13.5 cm

D. 18 cm

Answer :

Given : In the given figure, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at K and M respectively and EK = 9 cm


To Find : Perimeter of EDF


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


So, we have


KD = DH …[1]


[Tangents from point D]


HF = FM …[2]


[Tangents from point F]


Now Perimeter of Triangle PCD


= ED + DF + EF


= ED + DH + HF + EF


= ED + KD + FM + EF [From 1 and 2]


= EK + EM


Now,


EK = EM = 9 cm as tangents drawn from an external point to a circle are equal


So, we have


Perimeter = EK + EM = 9 + 9 = 18 cm

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