Two new sets of ellipse-related concyclic points (Q1037211)

The author describes an interesting result of planar Euclidean geometry. He studies a set of circles which can be associated with a general point \(P\) on an ellipse \(H\) and the ellipse itself. Some of these circles are generated by special points depending on \(P\) and \(H\) while \(P\) moves on \(H\) (e.g. the circles of Monge and of Barlotti), some belong to the position of \(P\) on \(H\). Concurrencies of some intersections of these circles with other circles or straight lines geometrically defined by \(P\) and \(H\) are described in the paper. The author works out interesting geometric coincidencies for some special points \(P\) on \(H\) (e.g. Fagano's point on \(H\)).