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X(1), X(7), X(57), X(527), X(1155), X(1156), X(1323), X(3321), X(10427)

isogonal conjugate of X(5526)

vertices of the intouch triangle

other points below

Geometric properties :

The Pelletier strophoid K040 and K806 generate a pencil of circular circum-cubics that contains the three pKs K949, K950, K951.

The singular focus of K949 is the midpoint X(15746) of X(1), X(2291).

K949 passes through :

• Q1 = X(15727) = X(7) / X(1156) = X(7)-Ceva conjugate of X(1156),

• Q2 = X(15728) = X(10427)* = X(6610)-isoconjugate of X(10427), on the circumcircle,

• Q3 = X(15729) = Q1*,

• Q4 = X(15730) = X(7) / X(1155),

• Q5 = Q4*,

• Q6 = X(7) / Q5.

Most of these points lie on several simple lines.