X(1), X(2), X(3), X(241), X(3229), X(5000), X(5001)
midpoints of ABC
Ka, Kb, Kc : centers of Apollonian circles
E1, E2 on the figure 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
Q026 is the quartic Q(X2) mentioned in page K1065 where other examples are given.