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In triangle geometry, a circumconic is a conic section that passes through the three vertices of a triangle,〔Weisstein, Eric W. "Circumconic." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Circumconic.html〕 and an inconic is a conic section inscribed in the sides, possibly extended, of a triangle.〔Weisstein, Eric W. "Inconic." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Inconic.htm〕 Suppose ''A,B,C'' are distinct non-collinear points, and let ''ΔABC'' denote the triangle whose vertices are ''A,B,C''. Following common practice, ''A'' denotes not only the vertex but also the angle ''BAC'' at vertex ''A'', and similarly for ''B'' and ''C'' as angles in ''ΔABC''. Let ''a'' = |''BC''|, ''b'' = |''CA''|, ''c'' = |''AB''|, the sidelengths of Δ''ABC''. In trilinear coordinates, the general circumconic is the locus of a variable point ''X'' = ''x'' : ''y'' : ''z'' satisfying an equation :''uyz + vzx + wxy'' = 0, for some point ''u : v : w''. The isogonal conjugate of each point ''X'' on the circumconic, other than ''A,B,C'', is a point on the line :''ux + vy + wz'' = 0. This line meets the circumcircle of ''ΔABC'' in 0,1, or 2 points according as the circumconic is an ellipse, parabola, or hyperbola. The ''general inconic'' is tangent to the three sidelines of ''ΔABC'' and is given by the equation :''u''2''x''2 + ''v''2''y''2 + ''w''2''z''2 − 2''vwyz'' − 2''wuzx'' − 2''uvxy'' = 0. ==Centers and tangent lines== 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「circumconic and inconic」の詳細全文を読む スポンサード リンク
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