A Feuerbach Type Theorem on Six Circles

摘要

   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.