# 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).

## Poster of the Japanese Theorem, Sangaku using iPad Apps

### Classroom Resource:Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

• To explore (show / hide): click/tap a check box.
• To stop/play the animation: click/tap the icon in the lower left corner.
• To go to first step: click/tap the "Go to step 1" button.
• To manipulate the interactive figure: click/tap and drag the points or figures.

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.