Let a convex inscribed polygon be
triangulated in any manner, and draw the incircle to each
triangle so constructed. Then the sum of the inradii is a
constant independent of the triangulation chosen. Hints:
Carnot's Theorem.
References: Fukagawa Hidetoshi, Tony Rothman, "Sacred
Mathematics: Japanese Temple Geometry" (Princenton
University Press, 2008).
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