Question

find the perimeter of the polygon if m∠a = m∠c. all the segments are tangent to circle o. 8 in, 9 in, 5 in, p = ? in

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 tangent segments are congruent.
Let the tangent segments from \(A\) be \(x\) and \(x\), from \(B\) be \(y\) and \(y\), from \(C\) be \(z\) and \(z\), from \(D\) be \(w\) and \(w\).
We know that \(w = 8\) (given \(AD\) - part), \(z=5\) (given \(CD\) - part), \(y = 9\) (given \(BC\) - part)

Step2: Calculate the perimeter of the quadrilateral

The perimeter \(P\) of quadrilateral \(ABCD\) is \(P=(8 + x)+(x + 9)+(9+5)+(5 + 8)\)
By the tangent - segment congruence property, we can also use the formula \(P = 2\times(8 + 9+5)\)

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Answer:

\(44\)