Sandor N. Kiss and Paul Yiu, The touchpoints triangles and the Feuerbach hyperbolas,
Forum Geometricorum, 14 (2014) 63--86.
Abstract. In this paper we generalize the famous Kariya theorem on the perspectivity of a given triangle with the homothetic images of the intouch triangle from the incenter to the touchpoints triangles of the excircles, leading to the triad of ex-Feuerbach hyperbolas. We also study in some details the triangle formed by the orthocenters of the touchpoints triangles. An elegant construction is given for the asymptotes of the Feuerbach hyperbolas.
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