Option B:
The perimeter of ΔABC is 28 units.
Solution:
AD = 5, DC = 6 and AB = 8
AD and AE are tangents to a circle from an external point A.
BE and BF are tangents to a circle from an external point B.
CD and CF are tangents to a circle from an external point C.
Tangents drawn from an external point to a circle are equal in length.
⇒ AD = AE, BE = BF and CD = CF
AE = 5
AE + BE = AB
5 + BE = 8
Subtract 5 from both sides.
BE = 3
BE = BF
⇒ BF = 3
CD = CF
⇒ CF = 6
Perimeter of the polygon = AE + BE + BF + CF + CD + AD
= 5 + 3 + 3 + 6 + 6 + 5
= 28
The perimeter of ΔABC is 28 units.
Option B is the correct answer.
