X(2), X(115), X(523), X(524), X(671), X(690), X(1648), X(5466)
vertices of the anticevian triangle of X(523)
E1 = X(5466), barycentric quotient of X(523) and X(524)
E2 = (b^2 - c^2)^2 / (b^2 + c^2 - 2a^2) : : , barycentric quotient of X(115) and X(524)
K239 is the pivotal cubic with pole X(115), the center of the Kiepert hyperbola, and pivot X(671), the antipode of the Steiner point X(99) on the Steiner ellipse. Its asymptotes are all real and are parallel to those of K240 = pK(X2, X892). Two of them are the lines X(99)X(524) and X(671)X(523) intersecting on the Steiner ellipse at the isotomic conjugate of X(543).
K239 meets the parabola (P) with perspector X(115) at A, B, C, X(523) and two other points E1 and E2. E1 is the intersection of the lines X(2)X(523) and X(671)X(690). E2 is the intersection of the lines X(115)X(523) and X(671)X(892). This parabola also contains X(476), X(685), X(850), X(892). Its axis is perpendicular to the Euler line.
See also K241.