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In the figure, a circle touches the side...

In the figure, a circle touches the side DF of `triangle EDF` at H and touches line ED and EF at points K and M respectively. If EK =9cm , then perimeter of `triangle EDF` is

A

18 cm

B

9 cm

C

13.5 cm

D

connot be determined

Text Solution

Verified by Experts

The correct Answer is:
A

Here EK=EM, DH=DK and FH and FM.
`" ""………"(" Tangent segment theorem ")`
Perimeter of `triangle EDF`
=ED+DF+EF
=ED+DH+HF+EF
=ED+DK+FM+EF
[DH=DK and HF=FM]
=EK+EM
=EK+EK[EK=EM]
=2EK
`=2xx9`
=18 cm
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