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X(1), X(2), X(3), X(15), X(16), X(17), X(18), X(39), X(2896), X(3413), X(3414)

midpoints of ABC

excenters

points of K655 on (O)

Q140 is a circular quartic passing through the X(5)-anticevian points. See Table 28.

There are 10 (not always all real) such points. They are represented in black and green on the figure.

For example, the nine-point center of the anticevian triangle of N' is N' itself. O' and H' are the corresponding circumcenter and orthocenter.

***

The singular focus of Q104 is X(2080).

Q140 has two real asymptotes parallel to those of the Kiepert hyperbola at X =

2a^4+b^4+c^4+4 b^2 c^2-4 a^2 b^2-4 a^2 c^2 : : ,

with SEARCH = 8.11132214901875.

X lies on the lines {99,754}, {194,6680}, {230,538}, {325,543}, etc.

X is now X(14148) in ETC (2017-08-21).

The remaining points on the sidelines of ABC are

{0 : -a^2+2 b^2+c^2 : a^2-b^2-2 c^2}, {2 a^2-b^2+c^2 : 0 : -a^2+b^2-2 c^2}, {2 a^2+b^2-c^2 : -a^2-2 b^2+c^2 : 0}.