Forum Geometricorum, 1 (2001) 173 -- 175.

Abstract: According to the famous Feuerbach theorem there exists a circle which is tangent internally to the incircle and externally to each of the excircles of a triangle. This is the nine-point circle of the triangle. We obtain a similar result by replacing the excircles with circles each tangent internally to the circumcircle and to the sides at the traces of a point.

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