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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 Harcourt's theorem ： ウィキペディア英語版 Harcourt's theorem Harcourt's theorem is a formula in geometry for the area of a triangle, as a function of its side lengths and the perpendicular distances of its vertices from an arbitrary line tangent to its incircle.〔.〕 The theorem is named after J. Harcourt, an Irish professor.〔.〕 ==Statement== Let a triangle be given with vertices ''A'', ''B'', and ''C'', opposite sides of lengths ''a'', ''b'', and ''c'', area ''K'', and a line that is tangent to the triangle's incircle at any point on that circle. Denote the signed perpendicular distances of the vertices from the line as ''a'' ', ''b'' ', and ''c'' ', with a distance being negative if and only if the vertex is on the opposite side of the line from the incenter. Then :$a\; a\; ^\backslash prime\; +\; b\; b^\backslash prime\; +\; c\; c^\backslash prime\; =\; 2K.$ 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「Harcourt'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.