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X(1), X(21), X(28), X(961), X(1610), X(1791), X(2217), X(2363), X(2975), X(16049), X(40452), X(40453), X(40454), X(40455), X(40456), X(40457)

on the figure P = X(40452) is the pivot

A'B'C' : circumcevian triangle of X(21)

PaPbPc : cevian triangle of P

Geometric properties :

P = X(40452) is the barycentric quotient X(1169) รท X(2217), a point on the lines {X1,X849}, {X21,X961}, {X28,X1791}, etc.

The locus of M whose anticevian triangle is perspective to the circumcevian triangle A'B'C' of X(21) is K379. The locus of the perspector is K1173.

The tangents to K1173 at A', B', C' concur at X(1610) on the cubic hence K1173 is a pK in A'B'C'. Its pivot is X(961) and its cevian triangle with respect to A'B'C' is A"B"C".

K1173 is a circumcevian pK. See CL072.