From the feet H_A, H_B, and H_C of each altitude of a triangle Δ A B C, draw lines (H_A P_A, H_A Q_A), (H_B P_B, H_B Q_B), (H_C P_C, H_C Q_C) perpendicular to the adjacent sides, as illustrated above. Then the points P_A, P_B, P_C, Q_A, Q_B, and Q_C are concyclic, and the circle passing through these points is called the Taylor circle. Here, P_A Q_A, P_B Q_B, and P_C Q_C are antiparallel to the sides B C, C A, and A B, respectively. Furthermore, the figures A H_C H H_B and A P_A H_A Q_A are similar, where H is the orthocenter of Δ A B C, P_A Q_A is parallel to H_B H_C, and P_A Q_A bisects H_A H_B and H_A H_C.

Taylor center | Tucker circles