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A tangential quadrilateral with its incircle. 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.
Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet. ... Tangential quadrilateral. Bicentric quadrilateral; Glyphs and symbols
Additionally, if a convex kite is not a rhombus, there is a circle outside the kite that is tangent to the extensions of the four sides; therefore, every convex kite that is not a rhombus is an ex-tangential quadrilateral. The convex kites that are not rhombi are exactly the quadrilaterals that are both tangential and ex-tangential. [16]
Ex-tangential quadrilateral – Convex 4-sided polygon whose sidelines are all tangent to an outside circle; Harcourt's theorem – Area of a triangle from its sides and vertex distances to any line tangent to its incircle; Circumconic and inconic – Conic section that passes through the vertices of a triangle or is tangent to its sides
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A tangential polygon is a polygon each of whose sides is tangent to a particular circle, called its incircle. Every triangle is a tangential polygon, as is every regular polygon of any number of sides; in addition, for every number of polygon sides there are an infinite number of non-congruent tangential polygons.
In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus. A rhombus is a tangential quadrilateral. [10] That is, it has an inscribed circle that is tangent to all four sides. A rhombus.
If the quadrilateral is a tangential quadrilateral, then its incenter also lies on this line. [3] See also. Complete quadrangle; Newton's theorem (quadrilateral)