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v w (v + w) (v^2 y - w^2 z) y z = 0

with u:v:w = cosA/2:cosB/2:cosC/2

X(7), X(174), X(177), X(234), X(2089), X(2091), X(7057)

vertices of the intouch triangle


K747 is the locus of P whose cevian triangle is perspective with the Tangential mid-arc triangle. See TCCT 6.15.

K747 is the pivotal cubic pK(X14596, X7).

K747 is also a pK with respect to the intouch triangle A'B'C' with pivot X(177), isopivot X(234).

The barycentric product of K747 by X(188) is K748, a similar cubic related with anticevian triangles.