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.

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