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infinite points of K024

Geometric properties :

K1137 is another example of stelloidal nK like K024, K094 and K1136.

Its radial center is X(381).

Its root R = X(34289) is the trilinear pole of the perpendicular bisector (L) of X(4) and X(23). R is also the isogonal conjugate of X(5063) hence it is a point on the Kiepert hyperbola.

Its pole Ω = X(34288) is the barycentric product X(6) x R, also the isogonal conjugate of X(15066), the isotomic conjugate of X(32833), the barycentric quotient X(32) ÷ X(5063).

K1137 is tritangent at A, B, C to the circumcircle (O) since it meets (O) at the same points as nK0(X6, X2). The three remaining common points of the two cubics lie on the line (D) passing through X(523), X(1351).

The tangentials Ta, Tb, Tc of A, B, C are collinear on the line (T) passing through X(1510).

The tangentials of the infinite points are obviously collinear on the satellite line (S) of the line at infinity.