Meaning of Japanese theorem | Babel Free

Definitions

1. A theorem stating that, no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant. Conversely, if the sum of inradii is independent of the triangulation, then the polygon is cyclic.
2. A theorem stating that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle.

CEFR level