Question

1) 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 = 9 cm then perimeter of triangle EDF = ?
​

Answer 1

Given :  circle touches the side DF of triangle EDF at H

and touches line ED and EF at points K and M respectively.

EK = 9 cm

To Find :  perimeter of triangle EDF = ?

Solution:

Perimeter of ΔEDF

= ED + DF + FE

DF  = DH + HF

=  ED + DH + HF + FE

DH = DK  ( equal tangent)

FH = FM  ( equal tangent)

=  ED + DK + FM + FE

= EK + EM

 EK = EM  ( Equal tangent)

= EK + EK

= 2 EK

EK = 9 cm

= 2 (9)

= 18  cm

Perimeter of ΔEDF  = 18 cm

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