the polygon circumscribes a circle. what is the perimeter of the polygon? the perimeter of the polygon is cm.

Explanation:

Step1: Recall tangent - segment property

If a polygon circumscribes a circle, then the lengths of the two - tangent segments drawn from an external point to the circle are equal. Let the polygon have vertices (A,B,C,D,\cdots) and the points of tangency of the circle with the sides of the polygon be (P,Q,R,S,\cdots). If we consider an external point (A) from which two tangent segments (AP) and (AS) are drawn to the circle, then (AP = AS).

Step2: Pair up the tangent - segments

Let's assume the given side - lengths are part of pairs of equal tangent segments. We have the following pairs of equal tangent segments: Let the side of length (5) cm and another non - shown side be equal, the side of length (8) cm and another non - shown side be equal, the side of length (9) cm and another non - shown side be equal, and the side of length (16) cm and another non - shown side be equal. The perimeter (P) of the polygon is the sum of all the side - lengths. [P=(5 + 5)+(8 + 8)+(9+9)+(16 + 16)] [P = 10+16 + 18+32] [P=76]

Answer:

76