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- Japanese_theorem_for_cyclic_quadrilaterals abstract "In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle.Triangulating an arbitrary concyclic quadrilateral by its diagonals yields four overlapping triangles (each diagonal creates two triangles). The centers of the incircles of those triangles form a rectangle.Specifically, let be an arbitrary concyclic quadrilateral and let be the incenters of the triangles . Then the quadrilateral formed by is a rectangle.Note that this theorem is easily extended to prove the Japanese theorem for cyclic polygons. To prove the quadrilateral case, simply construct the parallelogram tangent to the corners of the constructed rectangle, with sides parallel to the diagonals of the quadrilateral. The construction shows that the parallelogram is a rhombus, which is equivalent to showing that the sums of the radii of the incircles tangent to each diagonal are equal.The quadrilateral case immediately proves the general case by induction on the set of triangulating partitions of a general polygon.".
- Japanese_theorem_for_cyclic_quadrilaterals thumbnail Japanese_theorem_2.svg?width=300.
- Japanese_theorem_for_cyclic_quadrilaterals wikiPageExternalLink 4917.
- Japanese_theorem_for_cyclic_quadrilaterals wikiPageExternalLink mangho999.ps.
- Japanese_theorem_for_cyclic_quadrilaterals wikiPageExternalLink jap.shtml.
- Japanese_theorem_for_cyclic_quadrilaterals wikiPageExternalLink sangaku2.html.
- Japanese_theorem_for_cyclic_quadrilaterals wikiPageID "13940585".
- Japanese_theorem_for_cyclic_quadrilaterals wikiPageRevisionID "590750456".
- Japanese_theorem_for_cyclic_quadrilaterals hasPhotoCollection Japanese_theorem_for_cyclic_quadrilaterals.
- Japanese_theorem_for_cyclic_quadrilaterals subject Category:Euclidean_plane_geometry.
- Japanese_theorem_for_cyclic_quadrilaterals subject Category:Japanese_mathematics.
- Japanese_theorem_for_cyclic_quadrilaterals subject Category:Theorems_in_geometry.
- Japanese_theorem_for_cyclic_quadrilaterals type Abstraction100002137.
- Japanese_theorem_for_cyclic_quadrilaterals type Communication100033020.
- Japanese_theorem_for_cyclic_quadrilaterals type Message106598915.
- Japanese_theorem_for_cyclic_quadrilaterals type Proposition106750804.
- Japanese_theorem_for_cyclic_quadrilaterals type Statement106722453.
- Japanese_theorem_for_cyclic_quadrilaterals type Theorem106752293.
- Japanese_theorem_for_cyclic_quadrilaterals type TheoremsInGeometry.
- Japanese_theorem_for_cyclic_quadrilaterals comment "In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle.Triangulating an arbitrary concyclic quadrilateral by its diagonals yields four overlapping triangles (each diagonal creates two triangles). The centers of the incircles of those triangles form a rectangle.Specifically, let be an arbitrary concyclic quadrilateral and let be the incenters of the triangles .".
- Japanese_theorem_for_cyclic_quadrilaterals label "Japanese theorem for cyclic quadrilaterals".
- Japanese_theorem_for_cyclic_quadrilaterals label "Japanischer Satz für Sehnenvierecke".
- Japanese_theorem_for_cyclic_quadrilaterals label "Japanse stelling voor koordenvierhoeken".
- Japanese_theorem_for_cyclic_quadrilaterals label "Théorème japonais pour les quadrilatères inscriptibles".
- Japanese_theorem_for_cyclic_quadrilaterals label "مبرهنة يابانية في رباعي دائري".
- Japanese_theorem_for_cyclic_quadrilaterals sameAs Japanischer_Satz_für_Sehnenvierecke.
- Japanese_theorem_for_cyclic_quadrilaterals sameAs Théorème_japonais_pour_les_quadrilatères_inscriptibles.
- Japanese_theorem_for_cyclic_quadrilaterals sameAs Japanse_stelling_voor_koordenvierhoeken.
- Japanese_theorem_for_cyclic_quadrilaterals sameAs m.03cnvg1.
- Japanese_theorem_for_cyclic_quadrilaterals sameAs Q1683356.
- Japanese_theorem_for_cyclic_quadrilaterals sameAs Q1683356.
- Japanese_theorem_for_cyclic_quadrilaterals sameAs Japanese_theorem_for_cyclic_quadrilaterals.
- Japanese_theorem_for_cyclic_quadrilaterals wasDerivedFrom Japanese_theorem_for_cyclic_quadrilaterals?oldid=590750456.
- Japanese_theorem_for_cyclic_quadrilaterals depiction Japanese_theorem_2.svg.
- Japanese_theorem_for_cyclic_quadrilaterals isPrimaryTopicOf Japanese_theorem_for_cyclic_quadrilaterals.