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In geometry, the tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at the reference triangle's vertices. Thus the incircle of the tangential triangle coincides with the circumcircle of the reference triangle. The circumcenter of the tangential triangle is on the reference triangle's Euler line,〔 as is the center of similitude of the tangential triangle and the orthic triangle (whose vertices are at the feet of the altitudes of the reference triangle).〔Smith, Geoff, and Leversha, Gerry, "Euler and triangle geometry", ''Mathematical Gazette'' 91, November 2007, 436–452.〕〔 The tangential triangle is homothetic to the orthic triangle.〔Altshiller-Court, Nathan. ''College Geometry'', Dover Publications, 2007 (orig. 1952).〕 A reference triangle and its tangential triangle are in perspective, and the axis of perspectivity is the Lemoine axis of the reference triangle. That is, the lines connecting the vertices of the tangential triangle and the corresponding vertices of the reference triangle are concurrent.〔 The tangent lines containing the sides of the tangential triangle are called the exsymmedians of the reference triangle. Any two of these are concurrent with the third symmedian of the reference triangle.〔Johnson, Roger A., ''Advanced Euclidean Geometry'', Dover Publications, 2007 (orig. 1960).〕 The reference triangle's circumcircle, its nine-point circle, its polar circle, and the circumcircle of the tangential triangle are coaxal.〔 A right triangle has no tangential triangle, because the tangent lines to its circumcircle at its acute vertices are parallel and thus cannot form the sides of a triangle. ==See also== *Tangential quadrilateral *Tangential polygon 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「Tangential triangle」の詳細全文を読む スポンサード リンク
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