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K819

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X(6), X(69), X(74), X(524), X(6094)

X6-OAP points, see Table 53

P see below

(Peter Moses, private message 2016-09-17)

K819 is a member of the pencil of circular circum-cubics passing through the X6-OAP points.

Its singular focus F = X(14688) lies on the lines X(3)X(2854), X(6)X(1296) and on the circle C(X182, R/2).

The intersection P = X(14928) of the lines X(69)X(74), X(6)X(6094) also lies on K819.

The orthic line of K819 passes through X182, X524, X549, X1353.

Note that K819 meets :

• the circumcircle at the same points as the Neuberg cubic K001 hence must have three other collinear common points on the line X(2)X(2418),

• the line at infinity at the same points as the Droussent cubic K008 hence must have six other common points on a same circum-conic which passes through X(69), X(599).