Extend the symmedians of a triangle Δ A_1 A_2 A_3 to meet the circumcircle at P_1, P_2, P_3. Then the symmedian point K of Δ A_1 A_2 A_3 is also the symmedian point of Δ P_1 P_2 P_3. The triangles Δ A_1 A_2 A_3 and Δ P_1 P_2 P_3 are cosymmedian triangles, and have the same Brocard circle, second Brocard triangle, Brocard angle, Brocard points, and circumcircle.
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