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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kosnita's theorem ： ウィキペディア英語版 Kosnita's theorem In Euclidean geometry, Kosnita's theorem is a property of certain circles associated with an arbitrary triangle. Let $ABC$ be an arbitrary triangle, $O$ its circumcenter and $O\_a,O\_b,O\_c$ are the circumcenters of three triangles $OBC$, $OCA$, and $OAB$ respectively. The theorem claims that the three straight lines $AO\_a$, $BO\_b$, and $CO\_c$ are concurrent.〔 Their point of concurrence is known as the triangle's Kosnita point (named by Rigby in 1997). It is the isogonal conjugate of the nine-point center.〔〔 It is triangle center $X(54)$ in Clark Kimberling's list.〔 This theorem is special case of Dao's theorem on six circumcenters associated with a cyclic hexagon in.〔〔 == References == 〔 〔John Rigby (1997), ''Brief notes on some forgotten geometrical theorems.'' Mathematics and Informatics Quarterly, volume 7, pages 156-158 (as cited by Kimberling).〕 〔Darij Grinberg (2003), ''(On the Kosnita Point and the Reflection Triangle ).'' Forum Geometricorum, volume 3, pages 105–111. ISSN 1534-1178〕 〔Clark Kimberling (2014), ''(Encyclopedia of Triangle Centers )'', section ''X(54) = Kosnita Point''. Accessed on 2014-10-08〕 〔Nikolaos Dergiades (2014), ''(Dao’s Theorem on Six Circumcenters associated with a Cyclic Hexagon ).'' Forum Geometricorum, volume 14, pages=243–246. ISSN 1534-1178.〕 〔Telv Cohl (2014), ''(A purely synthetic proof of Dao's theorem on six circumcenters associated with a cyclic hexagon ).'' Forum Geometricorum, volume 14, pages 261–264. ISSN 1534-1178.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kosnita's theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.