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K798

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X(3), X(30), X(110), X(140), X(1385)

other points below

K798 is a focal cubic related with K463, K725.

Its singular focus is X(110) whose polar conic is the circle passing through X(3), X(110), X(140).

It is the locus of contacts of tangents drawn through X(110) to the circles passing through X(3), X(140).

K798 passes through :

• the common points Q1, Q2, Q3 of the cubic pK(X6, X140) and the circumcircle (apart A, B, C).

• the intersections R1, R2, R3 of the perpendicular bisector of X(110)X(140) with the sidelines of Q1Q2Q3.

• the six common points (labelled Ae, Ai, etc) of the perpendicular bisectors of ABC and the circles passing through X(5) whose centers are the corresponding midpoints of ABC.

See K725 for further details and a generalization.