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The Grebe triangle is defined and studied here. This page is only a compilation of various cubics and higher degree curves passing through its vertices G1, G2, G3 and other remarkable points. 



Cubics c denotes a circumcubic, otherwise the three remaining points on the circumcircle (O) are mentioned. Knnn* and Knnn*G denote the isogonal transforms of Knnn with respect to ABC and the Grebe triangle respectively. 



Note 1 : a pK passes through G1, G2, G3 if and only if its pole, pivot, isopivot lie on pK(X251 x X32, X251), K644, K177 respectively. Note 2 : any spK(P, Q = midpoint of X6,P) passes through G1, G2, G3 and X6. It also contains the infinite points of pK(X6, P) and the foci of the inconic with center Q. Its isogonal transform is spK(X6, Q). See CL055. This spK passes through P when P lies on the Grebe cubic K102. This spK is a K+ if and only if P lies on the circular cubic K837 passing through X(1), X(3), X(147), X(194), X(511), X(2930), X(7772). K643 is the most remarkable example obtained with P = X(3). Two other spK+ are listed with P = X(1), X(194), two points on K102. 



Higher degree curves Q019 is the only listed curve passing through the vertices of the Grebe triangle. Q019* is Q094. 
