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


Static Diagram of Dynamic Geometry 1480

Dynamic Problem 1480 Japanese Theorem for Cyclic Polygon, Triangulation, Non-intersecting Diagonals, Sum of Inradii, Invariant, Step-by-step Illustration, iPad Apps


Poster of Dynamic Geometry 1480 using iPad Apps

Dynamic Geometry 1480: Japanese Theorem for Cyclic Polygon, Triangulation, Non-intersecting Diagonals, Sum of Inradii, Invariant, Using GeoGebra, iPad Apps

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

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

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