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X(6), X(54), X(76), X(95), X(98), X(275), X(287), X(290), X(5012), X(10313), X(15407), X(18018), X(34536)

isogonal conjugates of X(40588), X(40601), X(52878), X(52967), X(60517), X(60524), X(60525), X(60526), X(60528), X(60595), X(60596)

points O1, O2 on (O) and on the trilinear polar of X(95), a line through X(323), X(401) and the isogonal conjugate of X(60517),

Geometric properties :

K1424 is the isogonal transform of K1355. It is pK(Ω, P) where :

• the pole Ω is the barycentric product of {54,290}, {95,98}, {275,287}, on the lines {54,1976}, {95,141}, {98,275}.

• the pivot P is the barycentric product of {216,232}, {276,287}, on the lines {54,276}, {95,98}.

K1424 meets the line at infinity at the same points as pK(X401, X76).

K1424 meets the circumcircle at the same points as pK(X248, X290). These are the isogonal transforms of the points where K1354 and K1355 meet the line at infinity.

A locus property :

Let M be the isogonal conjugate of X(60528), on K1424 and on the lines {4,54}, {22,76}, {95,160}, {98,237}, {99,2857}, {125,420}, {154,458}, {159,264}, etc.

M = a^8+a^6 b^2-a^4 b^4-a^2 b^6+a^6 c^2-a^4 b^2 c^2+a^2 b^4 c^2-b^6 c^2-a^4 c^4+a^2 b^2 c^4+2 b^4 c^4-a^2 c^6-b^2 c^6 : : , SEARCH = -5.63104109073413.

The anticevian triangle of P is perspective to the circumcevian triangle of M if and only if P lies on K1424. The locus of the perspector is a (not very interesting) pK with same pole.