Japanese theorem

proper noun

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.

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Meanings

proper nounthe Japanese theorem
  1. geometryA 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. geometryA theorem stating that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle.
Cite this entry
APA

Japanese theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/Japanese%20theorem

MLA

“Japanese theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Japanese%20theorem. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “Japanese theorem,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/Japanese%20theorem.

Source: Japanese theorem on Wiktionary, CC BY-SA 4.0.