The polygon circumscribes a circle. What is the perimeter of the polygon?
The perimeter of the polygon is?

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Polygons circumscribing a circle have tangents of equal lengths that come

from the same vertex that simplifies the calculation of the dimensions.

Reasons:

The polygon forms tangents to the circle, having the same external point

The lengths of the tangents drawn from the same external point are equal.

Therefore;

The length of the tangent on the other side of the tangent of given length and having the same external point are the same

Therefore, we have;

Two tangents of length 19 cm

Two tangents of length 9 cm

Two tangents of length 4 cm

and two tangents of length 6 cm

The above tangents reach round the perimeter of the polygon.

Therefore

The perimeter of the polygon = 19 + 19 + 6 + 6 + 4 + 4 + 9 + 9 = 76

The perimeter of the polygon = 76 cm

Learn more about tangents drawn from the same external point here:

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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