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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, which of the following is the perimeter of ΔEDF?

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9 cm

12 cm

13.5 cm

18 cm

answer is D.

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Detailed Solution

Given that, a circle touches the side DF of

Δ E D F

at H and touches ED and EF produced at K and M respectively and

E K = 9 cm .

We know that tangent segments to a circle from the same external point are congruent. Therefore,

E K = E M = 9 cm

and

E K + E M = 18 cm

⇒ E D + D K + E F + F M = 18 cm

⇒ E D + D H + E F + H F = 18 cm

(DK=DH and FM=FH)

⇒ E D + D F + E F = 18 cm

(DF = DH + HF)
Hence, the perimeter of ∆EDF is 18 cm.
Therefore, option 4 is correct.

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