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K870

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X(2), X(4), X(13), X(14), X(111), X(542), X(1648)

other points below

See Table 59 for other similar cubics and a generalization.

K870 is a focal cubic with singular focus F = X(14694), on the Euler line and also on X(511)X(1641), X(542)X(1648).

It is the locus of contacts of the tangents drawn through F to the circles passing through the Fermat points X(13), X(14).

The real asymptote is the homothetic of the Fermat axis (which is the orthic line of the cubic) under h(F, 2). The intersection X of the cubic with this asymptote also lies on the line X(2)X(99)X(111). X = X(14832) in ETC.

K870 passes through :

• Q1 = X(4)X(542) /\ X(111)X(1648), etc. Q1 = X(14833) in ETC.

• Q2 = X(2)X(542) /\ FQ1, etc. Q2 = X(14834) in ETC.

• Q3 = X(4)X(1648) /\ XQ2, etc.