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X(370) and its five mates, see Table 10

Ga, Gb, Gc : vertices of the antimedial triangle


extra points on Q036-A :

Ma midpoint of BC

A' reflection of A in BC

A" reflection of A' in Ma, on the circumcircle and on GbGc

The quintic Q036-A is the locus of point P such that its cevian triangle PaPbPc is isosceles at Pa. Q036-B and Q036-C are defined similarly. Obviously, these three quintics contain X(370) and its five mates.

Q036-A is a central curve with center Ma, the midpoint of BC. It has two nodes A and Ga. The nodal tangents at A are the bisectors and those at Ga are their parallels at Ga.

The "sum" of these three quintics is the quintic Q034.

See table 10 : X(370) related curves.