Circumcevian triangle
In Euclidean geometry, a circumcevian triangle is a special triangle associated with a reference triangle and a point in the plane of the triangle. It is also associated with the circumcircle of the reference triangle. Definition
[[File:CircumCevianTriangle.png|thumb|

{{legend-line|solid brown|Circumcevian triangle  is called the circumcevian triangle of  with reference to . Coordinates
Let  be the side lengths of triangle  and let the trilinear coordinates of  be . Then the trilinear coordinates of the vertices of the circumcevian triangle of  are as follows:

Some properties
Every triangle inscribed in the circumcircle of the reference triangle ABC is congruent to exactly one circumcevian triangle. The circumcevian triangle of P is similar to the pedal triangle of P.
The McCay cubic is the locus of point P such that the circumcevian triangle of P and ABC are orthologic. See also 

 Cevian
 Ceva's theorem

References

Triangle geometry