engleski

LOCUS OF INTERSECTIONS OF EULER LINES

Let A, B, and C be vertexes of a scalene triangle in the plane. Answering a recent problem by Jordan Tabov, we show that the locus of all points P with the property that the Euler lines of the triangles BCP, CAP, and ABP are concurrent is a subset of the union of the circumcircle and the Neuberg cubic of the triangle ABC. Some new properties of this remarkable cubic have also been discovered.

triangle; Euler line; concurrent lines; Neuberg cubic; isogonal conjugate

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