Japanese theorem
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English[edit]
Etymology[edit]
(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium.)
Proper noun[edit]
the Japanese theorem (geometry)
- 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.
- A theorem stating that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle.