In the given figure, a circle touches the side DF of ΔEDF at H and touches ED

Question:

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

(a) 18 cm                         (b) 13.5 cm                         (c) 12 cm                         (d) 9 cm                              [CBSE 2012]

Solution:

In the given figure, DH and DK are tangents drawn to the circle from an external point D.

∴ DH = DK                      (Lengths of tangents drawn from an external point to a circle are equal)

FH and FM are tangents drawn to the circle from an external point F.

∴ FH = FM                      (Lengths of tangents drawn from an external point to a circle are equal)

EK and EM are tangents drawn to the circle from an external point E.

∴ EM = EK = 9 cm          (Lengths of tangents drawn from an external point to a circle are equal)

Now,

Perimeter of ΔEDF = ED + DF + EF

                           = ED + (DH + FH) + EF

                           = ED + (DK + FM) + EF                (DH = DK and FH = FM)

                           = (ED + DK) + (FM + EF)

                           = EK + EM

                           = 9 cm + 9 cm

                           = 18 cm

Thus, the perimeter of ΔEDF is 18 cm.

Hence, the corrrect answer is option A.

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