Circumcevian 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'.
[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]
Reference triangle
△
ABC
Point
P
Circumcircle of
△
ABC
; lines between the vertices of
△
ABC
and
P
Circumcevian triangle
△
A'B'C'
of
P