If a polygon is both tangential and cyclic, it is called bicentric . ( All triangles are bicentric, for example . ) The incentre and circumcentre of a bicentric polygon are not in general the same point.
12.
If a polygon is both tangential and cyclic, it is called bicentric . ( All triangles are bicentric, for example . ) The incentre and circumcentre of a bicentric polygon are not in general the same point.
13.
If two circles, one within the other, are the incircle and the circumcircle of a bicentric quadrilateral, then every point on the circumcircle is the vertex of a bicentric quadrilateral having the same incircle and circumcircle.
14.
If two circles, one within the other, are the incircle and the circumcircle of a bicentric quadrilateral, then every point on the circumcircle is the vertex of a bicentric quadrilateral having the same incircle and circumcircle.
15.
Fuss's theorem, which is a generalization of Euler's theorem in geometry to a bicentric quadrilateral, says that if a quadrilateral is bicentric, then its two associated circles are related according to the above equations.
16.
Fuss's theorem, which is a generalization of Euler's theorem in geometry to a bicentric quadrilateral, says that if a quadrilateral is bicentric, then its two associated circles are related according to the above equations.
17.
The first and second Brocard points are one of many bicentric pairs of points, pairs of points defined from a triangle with the property that the pair ( but not each individual point ) is preserved under similarities of the triangle.
18.
In a bicentric quadrilateral, the inradius " r ", the circumradius " R ", and the distance " x " between the incenter and the circumcenter are related by Fuss'theorem according to
19.
In geometry, a "'bicentric polygon "'is a tangential polygon ( a polygon all of whose sides are tangent to an inner incircle ) which is also outer circle that passes through each vertex of the polygon.
20.
Since " eg " = " fh " if and only if the tangential quadrilateral is also cyclic and hence bicentric, this shows that the maximal area \ sqrt { abcd } occurs if and only if the tangential quadrilateral is bicentric.
