Dynamic Geometry 1480: Japanese Theorem for Cyclic Polygon, Sangaku, Triangulation, Non-intersecting Diagonals, Sum of Inradii, Invariant, Step-by-step Illustration

Let a cyclic polygon be triangulated in any manner by non-intersecting diagonals. Prove that the sum of the inradii of the triangles formed is a constant independent of the triangulation chosen (invariant).

Reference: Weisstein, Eric W. "Japanese Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JapaneseTheorem.html

Poster of Dynamic Geometry 1480 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 blue 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.