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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 Musselman's theorem ： ウィキペディア英語版 Musselman's theorem In Euclidean geometry, Musselman's theorem is a property of certain circles defined by an arbitrary triangle. Specifically, let $T$ be a triangle, and $A$, $B$, and $C$ its vertices. Let $A^$ *, $B^$ *, and $C^$ * be the vertices of the reflection triangle $T^$ *, obtained by mirroring each vertex of $T$ across the opposite side.〔 Let $O$ be the circumcenter of $T$. Consider the three circles $S\_A$, $S\_B$, and $S\_C$ defined by the points $A\backslash ,O\backslash ,A^$ *, $B\backslash ,O\backslash ,B^$ *, and $C\backslash ,O\backslash ,C^$ *, respectively. The theorem says that these three Musselman circles meet in a point $M$, that is the inverse with respect to the circumcenter of $T$ of the isogonal conjugate or the nine-point center of $T$.〔 The common point $M$ is the Gilbert point of $T$, which is point $X\_$ in Clark Kimberling's list of triangle centers.〔〔 == History == The theorem was proposed as an advanced problem by J. R. Musselman and R. Goormaghtigh in 1939,〔 and a proof was presented by them in 1941.〔 A generalization of this result was stated and proved by Goormaghtigh.〔 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「Musselman'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.