Question

8. In the figure, a circle touches the side DF of
AEDF at H and touches line ED and EF at points
K and M respectively. If EK =9 cm, then
perimeter of AEDF is
DH
(A) 18 cm
(C) 13.5 cm
(B) 9 cm
(D) cannot be determined​

Answer 1

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

Therefore, we have

EK = EM = 9 cm

Now, EK + EM = 18 cm

⇒ ED + DK + EF + FM = 18 cm

⇒ ED + DH + EF + HF = 18 cm (∵DK = DH and FM = FH)

⇒ ED + DF + EF = 18 cm

⇒ Perimeter of △EDF = 18 cm

Hence, the correct answer is option (d)