Japanese phrase for square tendons

The Japanese sentence (English. Japanese theorem ) states that in a quadrilateral the four center points of the inscribed circles of the four triangles that are characterized by triangulation with the diagonals result, the corners of a rectangle form.

Let be an arbitrary chordal quadrilateral and let be the centers of the incircles of the triangles . Then form a rectangle. ${\displaystyle \square ABCD}$ ${\displaystyle M_{1},M_{2},M_{3},M_{4}}$ ${\displaystyle \triangle ABD,\triangle ABC,\triangle CDB,\triangle CDA}$ ${\displaystyle M_{1},M_{2},M_{3},M_{4}}$

See also

• Carnot's theorem
• Sangaku
• Wasan
• Japanese phrase for concyclic polygons

Web links

Wikibooks: Evidence Archive - Japanese Theorem for Concyclic Quadrilaterals  - Learning and Teaching Materials

• Mangho Ahuja, Wataru Uegaki, Kayo Matsushita: In Search of the Japanese Theorem ( Memento of February 8, 2007 in the Internet Archive ) (English, Postscript file)
• Japanese sentence at Cut-the-Knot