![]() 12 Characterizations in the four subtriangles.The section characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to be able to have an incircle. An example of a quadrilateral that cannot be tangential is a non-square rectangle. Īll triangles can have an incircle, but not all quadrilaterals do. 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. Other less frequently used names for this class of quadrilaterals are inscriptable quadrilateral, inscriptible quadrilateral, inscribable quadrilateral, circumcyclic quadrilateral, and co-cyclic quadrilateral. Tangential quadrilaterals are a special case of tangential polygons. Since these quadrilaterals can be drawn surrounding or circumscribing their incircles, they have also been called circumscribable quadrilaterals, circumscribing quadrilaterals, and circumscriptible quadrilaterals. 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. In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides all can be tangent to a single circle within the quadrilateral. A tangential quadrilateral with its incircle
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