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In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an ''incircle''). This is a circle that is tangent to each of the polygon's sides. The dual polygon of a tangential polygon is a cyclic polygon, which has a circumscribed circle passing through each of its vertices. All triangles are tangential, as are all regular polygons with any number of sides. A well-studied group of tangential polygons are the tangential quadrilaterals, which include the rhombi and kites. ==Characterizations== A convex polygon has an incircle if and only if all of its internal angle bisectors are concurrent. This common point is the ''incenter'' (the center of the incircle).〔Owen Byer, Felix Lazebnik and Deirdre Smeltzer, ''Methods for Euclidean Geometry'', Mathematical Association of America, 2010, p. 77.〕 There exists a tangential polygon of ''n'' sequential sides ''a''1, ..., ''a''''n'' if and only if the system of equations : has a solution (''x''1, ..., ''x''''n'') in positive reals.〔 If such a solution exists, then ''x''1, ..., ''x''''n'' are the ''tangent lengths'' of the polygon (the lengths from the vertices to the points where the incircle is tangent to the sides). 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 polygon」の詳細全文を読む スポンサード リンク
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