∑ a^4 SA y^2 z^2
= a^2 b^2 c^2 x y z (x + y + z)
X(59), X(249), X(250), X(2065), X(10419)
extraversions of X(59)
infinite points of MacBeath circumconic
other points below
Q120 is the isogonal transform of the nine point circle (N) and the GSC transform the circumcircle.
Q120 is a circular quartic with singular focus X(2070), with three nodes at A, B, C where the nodal tangents concur at O and K.
The fourth point Oa of Q120 on the A-cevian line of O is the isogonal transform of the midpoint of AH, obviously on (N).
The fourth point Ka of Q120 on the A-symmedian is the isogonal transform of the second point of (N) on the median AG.
These six points Oa, Ob, Oc, Ka, Kb, Kc lie on a same conic (C).
Locus property :
A variable line L passing through O meets the sidelines of ABC at A', B', C'. Let A", B", C" be their respective inverses in (O). The lines AA", BB", CC" concur at Q on Q120.
It follows that the circles OAA', OBB', OCC' are in a same pencil. They meet at O and again at the inverse P of Q in (O). The locus of P is a tricircular sextic (see ADGEOM #3688).