Dynamic Geometry 1452: Japanese Theorem, Sangaku

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

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

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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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