Nikolaos Dergiades, Conics tangent at the vertices to two sides
of a triangle,
Forum Geometricorum, 10 (2010) 41--53.
Abstract: We study conics tangent to two sides of a given triangle at two
vertices, and construct two interesting triads of such conics, one consisting
of parabolas, the other rectangular hyperbolas. We also construct a new triangle
center, the barycentric cube root of X(25), which is the homothetic
center of the orthic and tangential triangles.