Dynamic Geometry 1452: Japanese Theorem, Sangaku

Given a cyclic quadrilateral ABCD and let A1, B1, C1, D1 the incenters and ra, rb, rc, rd the inradii of the triangles BAD, ABC, BCD, ADC. Then (1) A1B1C1,D1 is a rectangle, (2) ra + rc = rb + rd

This sangaku problem was proposed by Maruyama Ryoukan in 1800. References: Fukagawa Hidetoshi, Tony Rothman, "Sacred Mathematics: Japanese Temple Geometry" (Princenton University Press, 2008).

Static Diagram of the Japanese Theorem, Sangaku

Dynamic Geometry 1452: Japanese Theorem, Sangaku. Using GeoGebra



Poster of the Japanese Theorem, Sangaku using iPad Apps

Poster of Japanese Theorem, Sangaku, Dynamic Geometry. Using iPad

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Interactive step-by-step animation using GeoGebra

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