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K736

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X(3), X(40), X(376), X(7709)

vertices of the CircumNormal triangle

infinite points of K003

A'B'C' reflection of the Thomson triangle about O

other points below

K736 is the CircumNormal isogonal transform of K735 which is itself the CircumTangential isogonal transform of K078.

K736 is a stelloid with three real asymptotes parallel to those of the McCay cubic K003 at X = X(10304). X is the reflection of X(3524) about X(3) and lies on the Euler line.

The tangents at A', B', C' concur at X(376) hence K736 is a pK in A'B'C' and it must meet the sidelines of A'B'C' again at three points which are the vertices of a triangle perspective with A'B'C' at a point on the cubic which turns out to be O. It follows that K736 is the pK with pivot O, isopivot X(376) in A'B'C' but since X(376) is the orthocenter of A'B'C', K736 is the McCay cubic for A'B'C'. X is the centroid of A'B'C' since X(3524) is that of the Thomson triangle. Finally, since the McCay cubic in the Thomson triangle is K078, we obtain that K736 is the reflection of K078 about O. Hence, it contains the reflection of X(5373) about O and more generally, the reflections of all the points mentioned in the page K078.

K736 also contains the vertices of the pedal triangle of X(376) with respect to the CircumNormal triangle.

K736 is a member of the pencil of cubics generated by K725 and K735. This pencil also contains a circumcubic passing through X(3), X(4).