What is the perimeter of triangle ABC?

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.