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tangential quadrilateral
In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides are all tangent to a single circle within the quadrilateral. This circle is called the incircle of the quadrilateral or its inscribed circle, its center is the ''incenter'' and its radius is called the ''inradius''. Since these quadrilaterals can be drawn surrounding or circumscribing their incircles, they have also been called ''circumscribable quadrilaterals'', ''circumscribing quadrilaterals'', and ''circumscriptible quadrilaterals''.〔 Tangential quadrilaterals are a special case of tangential polygons.
Other, rarely used, names for this class of quadrilaterals are ''inscriptable quadrilateral'', ''inscriptible quadrilateral'', ''inscribable quadrilateral'', ''circumcyclic quadrilateral'', and ''co-cyclic quadrilateral''.〔〔Bryant, Victor and Duncan, John, "Wheels within wheels", ''Mathematical Gazette'' 94, November 2010, 502–505.〕 Due to the risk of confusion with a quadrilateral that has a circumcircle, which is called a cyclic quadrilateral or inscribed quadrilateral, it is preferable not to use any of the last five names.〔
All triangles have an incircle, but not all quadrilaterals do. An example of a quadrilateral that cannot be tangential is a non-square rectangle. The section characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to have an incircle.
==Special cases==
Examples of tangential quadrilaterals are the kites, which include the rhombi, which in turn include the squares. The kites are exactly the tangential quadrilaterals that are also orthodiagonal.〔.〕 If a quadrilateral is both tangential and cyclic, it is called a bicentric quadrilateral.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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