An equilateral triangleA bicentric kiteA bicentric isosceles trapezoidA regular pentagon
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, inscribed in an outer circle that passes through each vertex of the polygon. All triangles and all regular polygons are bicentric. On the other hand, a rectangle with unequal sides is not bicentric, because no circle can be tangent to all four sides.
In geometry, a bicentricpolygon is a tangential polygon (a polygon all of whose sides are tangent to an inner incircle) which is also cyclic — that is...
}{n}}\right)}}} For constructible polygons, algebraic expressions for these relationships exist; see Bicentricpolygon#Regular polygons. The sum of the perpendiculars...
In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle. The radii and centers of these...
For the circumradius-to-inradius ratio for various n, see Bicentricpolygon#Regular polygons. The same can be said of a regular polyhedron's insphere,...
Every regular polygon and every triangle is a cyclic polygon. A polygon that is both cyclic and tangential is called a bicentricpolygon. A hypocycloid...
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...
}{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...
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...
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...
such that the products of the lengths of the opposing sides are equal. Bicentric quadrilateral: it is both tangential and cyclic. Orthodiagonal quadrilateral:...
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...
each must be between sides of different lengths. All right kites are bicentric quadrilaterals (quadrilaterals with both a circumcircle and an incircle)...
equation given by Fuss' theorem, giving the relation among the radius of a bicentric quadrilateral's inscribed circle, the radius of its circumscribed circle...
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