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# Parry Circle

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

The Parry circle has circle function

 (1)

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

 (2)

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

 (3) (4)

(P. Moses, pers. comm., Jan. 1, 2005), where , , and 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 for (triangle centroid ) 15, 16 (first and second isodynamic points and ), 23 (far-out point), focus of the Kiepert parabola 110, Parry point 111 (Kimberling 1998, p. 227), as well as 352 and 353.

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

Isodynamic Points, Kiepert Parabola, Parry Point, Triangle Centroid

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## References

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Parry Point." http://faculty.evansville.edu/ck6/tcenters/recent/parry.html.

Parry Circle

## Cite this as:

Weisstein, Eric W. "Parry Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ParryCircle.html