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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).