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
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