Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides all...

an ex-tangential quadrilateral is a convex quadrilateral where the extensions of all four sides are tangent to a circle outside the quadrilateral. It has...

the quadrilateral is a tangential quadrilateral. Each diagonal of a rhombus bisects opposite angles. The excenter of an ex-tangential quadrilateral lies...

the incircle or inscribed circle. It is the special case of a tangential quadrilateral in which at least one pair of opposite sides are parallel. As for...

bicentric quadrilaterals have all the properties of both tangential quadrilaterals and cyclic quadrilaterals. Other names for these quadrilaterals are chord-tangent...

A bicentric quadrilateral is a cyclic quadrilateral that is also tangential and an ex-bicentric quadrilateral is a cyclic quadrilateral that is also...

Bicentric quadrilateral: it is both tangential and cyclic. Orthodiagonal quadrilateral: the diagonals cross at right angles. Equidiagonal quadrilateral: the...

a tangential quadrilateral the two pairs of opposite sides have the same total length. It is named after French engineer Henri Pitot. A tangential quadrilateral...

sides; that is, the kites are the tangential orthodiagonal quadrilaterals. A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides...

with any number of sides. A well-studied group of tangential polygons are the tangential quadrilaterals, which include the rhombi and kites. A convex polygon...

when convex, a tangential quadrilateral (its sides are tangent to an inscribed circle). The convex kites are exactly the quadrilaterals that are both orthodiagonal...

is both a kite and parallelogram is a rhombus. A rhombus is a tangential quadrilateral. That is, it has an inscribed circle that is tangent to all four...

sides there are an infinite number of non-congruent tangential polygons. A tangential quadrilateral ABCD is a closed figure of four straight sides that...

(See Quadrilateral#Remarkable points and lines in a convex quadrilateral.) Other collinearities of a tangential quadrilateral are given in Tangential...

excircle's center. Some (but not all) quadrilaterals have an incircle. These are called tangential quadrilaterals. Among their many properties perhaps...

opposite side extended, are collinear.: p. 149  An ex-tangential quadrilateral is a quadrilateral for which there exists a circle that is tangent to all...

every tangential quadrilateral other than a rhombus, the center of the incircle lies on the Newton line. Let ABCD be a tangential quadrilateral with at...

harmonic quadrilaterals since they have a circumcircle and each pair of opposite sides has the same two lengths. In a tangential quadrilateral (one with...

parallelogram) Lozenge Rhomboid Rectangle square (regular quadrilateral) Tangential quadrilateral Trapezoid or trapezium Isosceles trapezoid Pentagon Regular...

reference triangle is the Gergonne triangle of the tangential triangle. Tangential quadrilateral Tangential polygon Altshiller-Court, Nathan. College Geometry...

is a tangential quadrilateral. The circumscribed circle of a square passes through all four vertices, making the square a cyclic quadrilateral. Its radius...

In a tangential quadrilateral, the four angle bisectors concur at the center of the incircle. Other concurrencies of a tangential quadrilateral are given...

through each of the triangle's three vertices. A tangential polygon, such as a tangential quadrilateral, is any convex polygon within which a circle can...

triangle area formulas involving the semiperimeter also applies to tangential quadrilaterals, which have an incircle and in which (according to Pitot's theorem)...

closely related to the tangential quadrilaterals, ex-tangential quadrilaterals, and kites (which are both tangential and ex-tangential). Every antiparallelogram...

side-angle duality of polygons we compare properties of the cyclic and tangential quadrilaterals. This duality is perhaps even more clear when comparing an isosceles...

|d-c|<|b-a|<d+c.} The quadrilateral is a parallelogram when d − c = b − a = 0 {\displaystyle d-c=b-a=0} , but it is an ex-tangential quadrilateral (which is not...

circumscribed circle's center and the center of the excircle of an ex-tangential quadrilateral. Critical points of a cubic function and inflection points of a...

triangle Quadrilateral – 4 sides Cyclic quadrilateral Kite Rectangle Rhomboid Rhombus Square (regular quadrilateral) Tangential quadrilateral Trapezoid...

Cyclic quadrilateral – Quadrilateral whose vertices lie on a circle Cycloid – Curve traced by a point on a rolling circle Ex-tangential quadrilateral – Convex...