Japanese Theorem for Cyclic Polygons

The Japanese Theorem for Cyclic Polygons states that when a polygon inscribed in a circle is divided into triangles by drawing diagonals from a fixed set of vertices, the sum of the inradii of the resulting triangles is the same no matter which triangulation is chosen. It takes its name from its origin in Japanese temple geometry, the sangaku tradition of geometric problems inscribed on wooden tablets, and is a classical result illustrating an invariant hidden within an otherwise arbitrary choice of triangulation. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/