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Question
In the given figure, a circle touches the side DF of Δ EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the permeter of Δ EDF is
(a) 9 cm (b) 12 cm (c) 13.5 cm (d) 18 cm
In the given figure, a circle touches the side DF of Δ EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm then the permeter of Δ EDF is
(a) 9 cm (b) 12 cm (c) 13.5 cm (d) 18 cm
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Solution
We know that the tangent from an external point to the arced are equal
so
EK=EM=9cm
DK=DH
FH=FM
perimeter of ΔEDF
ED+EF+DF
ED+EF+DH+HF
(ED+DH)+(EF+HF)
(ED+DK)+(EF+FM)
EK+EM
9+9=18cm
correct option (d) 18cm
so
EK=EM=9cm
DK=DH
FH=FM
perimeter of ΔEDF
ED+EF+DF
ED+EF+DH+HF
(ED+DH)+(EF+HF)
(ED+DK)+(EF+FM)
EK+EM
9+9=18cm
correct option (d) 18cm
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