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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 Circle of antisimilitude ： ウィキペディア英語版 Circle of antisimilitude In geometry, the circle of antisimilitude (also known as mid-circle) of two circles, ''α'' and ''β'', is a circle for which ''α'' and ''β'' are inverses of each other. If ''α'' and ''β'' are non-intersecting or tangent, there exists one circle of antisimilitude; if ''α'' and ''β'' intersect at two points, there exist two circles of antisimilitude. When ''α'' and ''β'' are congruent, the circle of antisimilitude is degenerate; it becomes a line of symmetry, in which ''α'' and ''β'' are reflections of each other.〔.〕〔.〕 ==Properties== If the two circles ''α'' and ''β'' cross each other, another two circles ''γ'' and ''δ'' are each tangent to both ''α'' and ''β'', and in addition ''γ'' and ''δ'' are tangent to each other, then the point of tangency between ''γ'' and ''δ'' necessarily lies on one of the two circles of antisimilitude. If ''α'' and ''β'' are disjoint and non-concentric, then the locus of points of tangency of ''γ'' and ''δ'' again forms two circles, but only one of these is the (unique) circle of antisimilitude. If ''α'' and ''β'' are tangent or concentric, then the locus of points of tangency degenerates to a single circle, which again is the circle of antisimilitude.〔(Tangencies: Circular Angle Bisectors ), The Geometry Junkyard, David Eppstein, 1999.〕 If the two circles ''α'' and ''β'' cross each other, then their two circles of antisimilitude each pass through both crossing points, and bisect the angles formed by the arcs of ''α'' and ''β'' as they cross. If a circle ''γ'' crosses circles ''α'' and ''β'' at equal angles, then ''γ'' is crossed orthogonally by one of the circles of antisimilitude of ''α'' and ''β''; if ''γ'' crosses ''α'' and ''β'' in supplementary angles, it is crossed orthogonally by the other circle of antisimilitude, and if ''γ'' is orthogonal to both ''α'' and ''β'' then it is also orthogonal to both circles of antisimilitude.〔 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「Circle of antisimilitude」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.