Q: The polygon circumscribes the circle. Find the perimeter.
Circle and a quadrilateral
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$\begingroup$
geometry
circles
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0I'm looking for the perimeter of the square, and I don't ever remember seeing this problem. – 2012-12-16
2 Answers
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It is a fact that any two intersecting tangents are equal in length.
Thus, the perimeter is $2(9+7+5+8)=58$
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It's a basic theorem in euclidean geometry: a quadrilateral circumscribes a circle iff the sum of the lengths of both pairs of opposite sides is the same. This follows at once from the fact that Amr reminds in his answers: both tangents to a circle from an exterior point to the circle have the same length.
From this the perimeter of your quadrilateral is 58.