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    Grebe Point

    Alternate names
    Definition

    The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian point is the isogonal conjugate of the triangle centroid G. In other words, let G be the triangle centroid of a triangle Δ A B C, A M_A, B M_B, and C M_C the medians of Δ A B C, A L_A, B L_B, and C L_C the angle bisectors of angles A, B, C, and A K_A, B K_B, and C K_C the reflections of A M_A, B M_B, and C M_C about A L_A, B L_B, and C L_C. Then K is the point of concurrence of the lines A K_A, B K_B, and C K_C. According to Honsberger, the symmedian point is "one of the crown jewels of modern geometry." The symmedian point is Kimberling center X_6.

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