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 ______.

Options

• 9 cm

• 12 cm

• 13.5 cm

• 18 cm

Answer 1

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 18 cm.

Explanation:

Tangents from the same external point are equal.

Let DK = DH = x and FM = FH = y and EK = EM = 9.

Then ED = EK – DK

= 9 – x

EF = EM – FM

= 9 – y

DF = DH + HF

= x + y

Perimeter = ED + DF + EF

= (9 – x) + (x + y) + (9 – y)

= 18 cm