The figure shows a
cyclic
quadrilateral ABCD. E, F, G, and H are the
incenters and r_{a},
r_{b}, r_{c}, and r_{d} are the
inradii
of the triangles ABD, ABC, BCD and ACD respectively. Prove that
EFGH is a rectangle and r_{a} + r_{c} = r_{b}
+ r_{d}. See the
proof.
References: Fukagawa Hidetoshi, Tony Rothman, "Sacred
Mathematics: Japanese Temple Geometry" (Princenton
University Press, 2008).
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