If the pedal triangle of a point P in a triangle Δ A B C is a Cevian triangle, then the point P is called the pedal-cevian point of Δ A B C with respect to the pedal triangle. The circumcenter O, orthocenter H, and incenter I of a triangle Δ A_1 A_2 A_3 are always pedal-Cevian points, with corresponding pedal triangles given by the medial triangle Δ M_1 M_2 M_3, orthic triangle Δ H_1 H_2 H_3, and contact triangle Δ T_1 T_2 T_3, respectively, and pedal points the triangle centroid G, orthocenter H, and Gergonne point Ge, respectively. If P is a pedal-Cevian point of a triangle, then so is its isotomic conjugate Q, as is its reflection P' in the circumcenter.
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