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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.

Let P be a point in the plane of the reference triangle △*ABC*. Let the lines AP, BP, CP intersect the circumcircle of △*ABC* at A', B', C'. The triangle △*A'B'C'* is called the **circumcevian triangle** of P with reference to △*ABC*.^{[1]}

Let a,b,c be the side lengths of triangle △*ABC* and let the trilinear coordinates of P be *α* : *β* : *γ*. Then the trilinear coordinates of the vertices of the circumcevian triangle of P are as follows:^{[2]}

- Every triangle inscribed in the circumcircle of the reference triangle ABC is congruent to exactly one circumcevian triangle.
^{[2]} - The circumcevian triangle of P is similar to the pedal triangle of P.
^{[2]} - The McCay cubic is the locus of point P such that the circumcevian triangle of P and ABC are orthologic.
^{[3]}

**^**Kimberling, C (1998). "Triangle Centers and Central Triangles".*Congress Numerantium*.**129**: 201.- ^
^{a}^{b}^{c}Weisstein, Eric W. ""Circumcevian Triangle"".*From MathWorld--A Wolfram Web Resource*. MathWorld. Retrieved 24 December 2021. **^**Bernard Gilbert. "K003 McCay Cubic".*Catalogue of Triangle Cubics*. Bernard Gilbert. Retrieved 24 December 2021.