find the perimeter of the polygon if ∠b≅∠d. p = ? cm

Explanation:

Step1: Recall tangent - secant property

If two tangents are drawn from an external point to a circle, then the lengths of the two tangents are equal. Since (\angle B\cong\angle D), let the lengths of the tangents from (A), (B), (C), and (D) to the circle be considered. Let the length of the tangent from (A) to the circle be (x), from (B) be (y), from (C) be (z), and from (D) be (w). We know that if we consider the pairs of tangents from each vertex to the circle, we have the following equal - length relationships.

Step2: Identify equal - length segments

Let the side (AB = 6.5) cm, (BC = 7.5) cm, (CD = 8.5) cm. If we assume the lengths of the tangents from (A), (B), (C), and (D) to the circle, we can find that the perimeter (P) of the quadrilateral can be calculated as (P=2(AB + CD)) (by the property of tangents from external points to a circle).

Step3: Calculate the perimeter

Substitute (AB = 6.5) cm and (CD = 8.5) cm into the formula (P = 2(AB+CD)). [ \begin{align*} P&=2(6.5 + 8.5)\ &=2\times15\ &=30 \end{align*} ]

Answer:

30