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X(1281), X(8852), X(16360), X(16361), X(16364), X(16365)

vertices of both Sharygin triangles

Geometric properties :

K962 is the unique cubic passing through the vertices of the reference triangle ABC and the vertices of both Sharygin triangles A1B1C1, A2B2C2.

K962 meets the sidelines of A1B1C1 again at A3, B3, C3 and those of A2B2C2 again at A4, B4, C4. The triangles A3B3C3 and A4B4C4 are perspective at P = X(16364) which lies on K962.

Q = X(16365) is the third point of K962 on the line X(1281), X(8852) also passing through X(75).

Note that X(16360), X(16361) are the nineth common points of K962 and the cubics K960, K961 respectively.