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In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle. The radii and centers of these...

In geometry, a bicentric polygon is a tangential polygon (a polygon all of whose sides are tangent to an inner incircle) which is also cyclic — that is...

hence bicentric, this shows that the maximal area a b c d {\displaystyle {\sqrt {abcd}}} occurs if and only if the tangential quadrilateral is bicentric. A...

and cyclic, it is called bicentric. (All triangles are bicentric, for example.) The incentre and circumcentre of a bicentric polygon are not in general...

exradius is maximum when the quadrilateral is also cyclic (and hence an ex-bicentric quadrilateral). These formulas explain why all parallelograms have infinite...

Woo circles Circle-derived entities Apollonian gasket Arbelos Bicentric polygon Bicentric quadrilateral Coxeter's loxodromic sequence of tangent circles...

cyclic polygon. A polygon that is both cyclic and tangential is called a bicentric polygon. A hypocycloid is a curve that is inscribed in a given circle...

concentric. For the circumradius-to-inradius ratio for various n, see Bicentric polygon#Regular polygons. The same can be said of a regular polyhedron's...

right angles – a right kite. A bicentric quadrilateral is a cyclic quadrilateral that is also tangential and an ex-bicentric quadrilateral is a cyclic quadrilateral...

defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential...

other are called bicentric polygons, so this special case of Poncelet's porism can be expressed more concisely by saying that every bicentric polygon is part...

such that the products of the lengths of the opposing sides are equal. Bicentric quadrilateral: it is both tangential and cyclic. Orthodiagonal quadrilateral:...

Poncelet–Steiner theorem Polygon triangulation Pons asinorum Quadrilateral Bicentric quadrilateral Cyclic quadrilateral Equidiagonal quadrilateral Kite (geometry)...

circumscribe one circle and are inscribed in another circle, they are bicentric quadrilaterals (actually tricentric, as they also have a third circle...

}{2}}\right)}},} in which α and γ are two opposite angles. The four sides of a bicentric quadrilateral are the four solutions of a quartic equation parametrized...

America. Third Brocard Point at MathWorld Bicentric Pairs of Points and Related Triangle Centers Bicentric Pairs of Points Bicentric Points at MathWorld...

similar remarks apply. The first and second Brocard points are one of many bicentric pairs of points, pairs of points defined from a triangle with the property...

isosceles trapezoid is cyclic, an isosceles tangential trapezoid is a bicentric quadrilateral. That is, it has both an incircle and a circumcircle. If...

pentagon Salinon Semicircle Squircle Steiner chain Tangential quadrilateral Bicentric quadrilateral Borromean rings Crescent Vesica piscis Arc Caustic Cissoid...

coordinates ξ and η can be expressed as elliptic functions of u. The bicentric problem has a constant of motion, namely, r 1 2 r 2 2 d θ 1 d t d θ 2...