too complicated to be written here. Click on the link to download a text file.
other points described below
K374 is the isogonal transform of K037, the Tixier equilateral cubic.
Hence, it meets the circumcircle at A, B, C and three other points X(74), Z1, Z2 which are the vertices of an equilateral triangle.
Z1 and Z2 are isoconjugates on the curve and their barycentric product is X(50). Their midpoint is X(1511). The tangents at these two points and at the pivot X(1511) pass through X(110).
In fact, the polar conic of X(110) is the union of the line X(526)X(X1511) (which contains Z1 and Z2) and the Brocard axis.
Note that the polar conics of the isodynamic points X(15), X(16) are each also decomposed into two lines and these lines are perpendicular. It follows that each point on the Brocard axis has a polar conic which is a rectangular hyperbola.
Notes on X(1511) = Fermat crosssum
– from Clark's ETC
– other notes