Japanese Circumscribed Quadrilateral Theorem and its Generalization

[Michael de Villiers]

This dynamic, interactive sketch at http://dynamicmathematicslearning.com/japanese-circum-quad-theorem.html shows the following beautiful Japanese Temple Geometry result, "The products of the radii of the excircles on each pair of opposite sides of a circumscribed quadrilateral are equal", as well as its generalization to circumscribed 2n-gons. Can you explain why (prove) that the result and its generalization is true?

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