Nguyen Thanh Dung, Some circles associated with the Feuerbach points,
Forum Geometricorum, 14 (2014) 403--408.
Abstract. Consider a triangle with its nine-point circle tangent to the incircle and excircles at the Feuerbach point. We show that the four circles each through the circumcenter, nine-point, and Feuerbach point contain the nine-point center of the intouch triangle or the corresponding extouch triangle. Furthermore, the lines joining these Feuerbach points to the corresponding nine-point centers are concurrent on the nine-point circle of the given triangle.
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