The circumcenter has trilinears cos ⁡ A : cos ⁡ B : cos ⁡ C , {\displaystyle \cos A:\cos B:\cos C,} corresponding to the parameter value t = 0. {\displaystyle t=0.} The centroid has trilinears cos ⁡ A + cos ⁡ B cos ⁡ C : cos ⁡ B + cos ⁡ C cos ⁡ A : cos ⁡ C + cos ⁡ A cos ⁡ B , {\displaystyle \cos A+\cos B\cos C:\cos B+\cos C\cos A:\cos C+\cos A\cos B,} corresponding to the parameter value t = 1. {\displaystyle t=1.} The nine-point center has trilinears cos ⁡ A + 2 cos ⁡ B cos ⁡ C : cos ⁡ B + 2 cos ⁡ C cos ⁡ A : cos ⁡ C + 2 cos ⁡ A cos ⁡ B , {\displaystyle \cos A+2\cos B\cos C:\cos B+2\cos C\cos A:\cos C+2\cos A\cos B,} corresponding to the parameter value t = 2. {\displaystyle t=2.} The de Longchamps point has trilinears cos ⁡ A − cos ⁡ B cos ⁡ C : cos ⁡ B − cos ⁡ C cos ⁡ A : cos ⁡ C − cos ⁡ A cos ⁡ B , {\displaystyle \cos A-\cos B\cos C:\cos B-\cos C\cos A:\cos C-\cos A\cos B,} corresponding to the parameter value t = − 1. {\displaystyle t=-1.}