Go Geometry Problem Sangaku Geometry Theorem: Cyclic Quadrilateral

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 world's first Interactive Symbolic Geometry System. This means: Geometric figures can be defined by either Symbolic Constraints or numeric locations.

You can download Geometry Expressions 2 Free Trial. It is a fully featured 30 day evaluation copy of the software. All constraints, constructions and measurements are available for you to use.
 

 

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Last updated: July 17, 2009