Question

Find the perimeter of the polygon. Assume that lines which appear to be tangent are tangent. Round to the nearest tenth if necessary.

Answer 1

The perimeter of the polygon is 53.6 units.

Solution:

The reference image to the answer is attached below.

AP = 8, BQ = 7.8 and CR = 11

AP and AR are tangents to a circle from an external point A.

BP and BA are tangents to a circle from an external point B.

CQ and CR are tangents to a circle from an external point C.

Tangents drawn from an external point to a circle are equal in length.

⇒ AP = AR, BP = BQ and CQ = CR

AR = 8

BP = BQ

⇒ BP = 7.8

CQ = CR

⇒ CQ = 11

Perimeter of the polygon = AP + BP + BQ + CQ + CR + AR

                                          = 8 + 7.8 + 7.8 + 11 + 11 + 8

                                          = 53.6

The perimeter of the polygon is 53.6 units.