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The figure shows a
cyclic
quadrilateral ABCD. E, F, G, and H are the
incenters and ra,
rb, rc, and rd are the
inradii
of the triangles ABD, ABC, BCD and ACD respectively. Prove that
EFGH is a rectangle and ra + rc = rb
+ rd. See the
proof.
References: Fukagawa Hidetoshi, Tony Rothman, "Sacred
Mathematics: Japanese Temple Geometry" (Princenton
University Press, 2008).
I have used
Geometry Expressions to visualize these geometric forms and
check out a variety of conjectures. Geometry Expressions is the
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or numeric locations.
You can
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2 Free Trial. It is a fully
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