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X(1), X(2), X(3), X(241), X(3229), X(5000), X(5001) midpoints of ABC excenters Ka, Kb, Kc : centers of Apollonian circles E1, E2 are X(5000), X(5001) 

The tangents at A, B, C are the medians and those at the in/excenters pass through O. The fourth point on AI is b + c : b : c and the fourth point on IbIc is b  c : b : c.
Locus properties :
Q026 is the locus of point P such that

