Answer:
Perimeter of the polygon is 76 cm
Step-by-step explanation:
There is a fact in the circle, the two tangents drawn from a point out side the circle are equal in length
Let us use this fact to solve the problem
∵ AB and AH are tangents to the circle
∵ A is out side the circle
∴ AB = AH
∵ AB = 9 cm
∴ AH = 9 cm
∵ CB and CD are tangents to the circle
∵ C is out side the circle
∴ CB = CD
∵ CB = 19 cm
∴ CD = 19 cm
∵ ED and EF are tangents to the circle
∵ E is out side the circle
∴ ED = EF
∵ EF = 6 cm
∴ ED = 6 cm
∵ GF and GH are tangents to the circle
∵ G is out side the circle
∴ GF = GH
∵ GF = 4 cm
∴ GH = 4 cm
The perimeter of the polygon is the sum of the lengths of its sides
∵ The sides of polygon ACEG are AC, CE, EG, and GA
∵ AC = 9 + 19 = 28 cm
∵ CE = 19 + 6 = 25 cm
∵ EG = 4 + 6 = 10 cm
∵ GA = 4 + 9 = 13 cm
∴ Perimeter of the polygon = 28 + 25 + 10 + 13
∴ Perimeter of the polygon = 76 cm