Question

find the perimeter of the polygon if \\( \angle b \cong \angle d \\).
\\( p = ? \mathrm { cm } \\)

Explanation:

Step1: Use the property of tangents from a common external point

If two tangent segments are drawn from an external point to a circle, then the two segments are congruent.
Since \(\angle B\cong\angle D\), the lengths of the tangent segments from \(A\) are equal, and the lengths of the tangent segments from \(C\) are equal.
Let the length of the tangent from \(A\) be \(x = 11.5\) cm and the length of the tangent from \(C\) be \(y=12.5\) cm.

Step2: Calculate the perimeter of the polygon

The perimeter \(P\) of the quadrilateral \(ABCD\) is \(P = 2x + 2y\).
Substitute \(x = 11.5\) and \(y = 12.5\) into the formula:

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Answer:

\(48\)