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About: Musselman's theorem     Goto   Sponge   NotDistinct   Permalink

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In Euclidean geometry, Musselman's theorem is a property of certain circles defined by an arbitrary triangle. Specifically, let be a triangle, and , , and its vertices. Let , , and be the vertices of the , obtained by mirroring each vertex of across the opposite side. Let be the circumcenter of . Consider the three circles , , and defined by the points , , and , respectively. The theorem says that these three Musselman circles meet in a point , that is the inverse with respect to the circumcenter of of the isogonal conjugate or the nine-point center of .