Triplets of mutually orthogonal circles associated with any ellipse

Abstract

The author has shown (J. Geom. 94, 159–173, 2009) that, for any general point P on a given ellipse H, four concyclic notable points exist which determine a circle (denoted by Ω) orthogonal to Monge’s circle. Now, it is shown that a new set of notable concyclic points exists; such points determine a circle (denoted by Δ) orthogonal to both Monge’s circle and the circle Ω. Moreover, it is possible to introduce a new ellipse (denoted by H _Δ) concentric with the circle Δ, which is tangent to the ellipse H at P, shares the same circle Ω with the ellipse H and admits the circle Δ as its own Monge’s circle. Only elementary facts from trigonometry and analytic geometry are used.