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X(6), X(9), X(86), X(1100), X(1213), X(1839), X(2160)

midpoints of ABC

K207 = Kw(X1) is the locus of poles of pK+ with pivot X(1). It is a member of the class CL017 of cubics.

The tangents at A, B, C concur at X(2308) = a^2(b + c + 2a) : : , not on the curve.

For example, pK+(X6, X1) is the union of the internal bisectors, pK+(X9, X1) = K157, pK+(X2160, X1) = K097 is also equilateral, pK+(X1213, X1) is a pK++ with center X(1125).

 

K207 is also psK(X2308, X2, X6) in Pseudo-Pivotal Cubics and Poristic Triangles.

Compare K207 and Kw(X4) = K208 = psK(X5 x X393, X2, X53).