Two new sets of ellipse-related concyclic points

Abstract

Two new circles (denoted by Γ _I and Γ _E ) are shown to be associated with any ellipse. Their analogies with two circles described by Barlotti are described. Two further new circles—denoted by Ω and Γ—are shown to be associated with any general point P of the ellipse. Tight relationships link the circles Ω and Γ with the circle K (previously introduced by the present author), as well as with Monge’s orthoptic circle, with Barlotti’s circles and with the circles Γ _I and Γ _E . In particular, the circle Ω is orthogonal to Monge’s circle. A new special point of the ellipse (the point T) is described. New properties of Fagnano’s point are described.