Parry Circle


The circle passing through the isodynamic points S and S^' and the triangle centroid G of a triangle DeltaA_1A_2A_3 (Kimberling 1998, pp. 227-228).

The Parry circle has circle function


which does not correspond to any noted triangle center. The center has triangle center function


which is Kimberling center X_(351) (Kimberling 1998, p. 232), and the radius is


(P. Moses, pers. comm., Jan. 1, 2005), where S_A, S_B, and S_C is Conway triangle notation.


The Parry circle and the circumcircle of a triangle intersect in two points: the focus of the Kiepert parabola and the so-called Parry point.

The Parry circle passes through Kimberling centers X_i for i=2 (triangle centroid G) 15, 16 (first and second isodynamic points S and S^'), 23 (far-out point), focus of the Kiepert parabola 110, Parry point 111 (Kimberling 1998, p. 227), as well as 352 and 353.


It is orthogonal to the Brocard circle, circumcircle, Lucas circles radical circle, and Lucas inner circle.

Furthermore, the common chord determined by these points also passes through the symmedian point of the original triangle (Kimberling).

See also

Isodynamic Points, Kiepert Parabola, Parry Point, Triangle Centroid

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Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Parry Point."

Referenced on Wolfram|Alpha

Parry Circle

Cite this as:

Weisstein, Eric W. "Parry Circle." From MathWorld--A Wolfram Web Resource.

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