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X(1), X(3), X(4) excenters midpoints antipodes of A, B, C other points below 

Denote by PaPbPc the pedal triangle of point P and by T1, T2, T3, T4, T5, T6 the areas of triangles PBPa, PPaC, PCPb, PPbA, PAPc, PPcB respectively. Let M1 and M2 be one of the means of T1, T3, T5 and T2, T4, T6 respectively. We seek the locus L of P such that M1 = M2. When the means are :
Recall that the McCay cubic K003 is the locus of P such that T1*T3+T3*T5+T5*T1 = T2*T4+T4*T6+T6*T2. Q082 contains the 24 following points :
The 21 common points of the Darboux cubic and Q082 are clearly identified. 
