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A cyclic polygon is one that can be inscribed in a circle. It is fairly easy to construct a cyclic quadrilateral with two sides with integer length a and two sides with integer length b such that the radius of the circle is also an integer (for example, a 6×8 or a 10×24 rectangle).
This month's problem is to find a cyclic pentagon having three sides with integer length a and two sides with integer length b such that the radius of the circle is also an integer. Can you find an infinite family of (non-similar) pentagons with this property?
The solution will be posted shortly.
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