The Parry circle and the circumcircle of triangle △ABC intersect in two points. One of them is a focus of the Kiepert parabola of △ABC.[3] The other point of intersection is called the Parry point of △ABC.
The trilinear coordinates of the Parry point are
The point of intersection of the Parry circle and the circumcircle of △ABC which is a focus of the Kiepert hyperbola of △ABC is also a triangle center and it is designated as X(110) in Encyclopedia of Triangle Centers. The trilinear coordinates of this triangle center are
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