On Six Collinear Points in Bicentric Quadrilaterals

Abstract

Summary We generalize the concept of the Bevan point and the Bevan circle to a special sort of quadrilateral, so-called bicentric quadrilaterals, which have—like triangles—both an incenter and a circumcenter. As with triangles, the Bevan point V is the reflection of the incenter I over the circumcenter O. There are three other known points on the straight line through V, I, O, thus giving at least six collinear points on this straight line. We also deal with special homotheties, giving primarily synthetic and elementary proofs.