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The Parry reflection point is the triangle center where three reflected lines concur. Draw lines through the vertices , , and of a triangle parallel to its Euler line, then reflect them in the opposite sidelines , , and , respectively. It is Kimberling center and has triangle center function

When defined, the composition of two isogonal conjugations with inversion in the circumcircle between them carries the Parry reflection point to Point Alrescha (Kimberling, X(1117)).

See also

Euler Line, Parry Point, Reflection

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References

Kimberling, C. "Encyclopedia of Triangle Centers: X(399)=Parry Reflection Point." https://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X399.Kimberling, C. "Encyclopedia of Triangle Centers: X(1117)=Point Alrescha." https://faculty.evansville.edu/ck6/encyclopedia/ETCPart2.html#X1117.Parry, C. "Problem 10637." Amer. Math. Monthly 105, 68, 1998.

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Parry Reflection Point

Cite this as:

Weisstein, Eric W. "Parry Reflection Point." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ParryReflectionPoint.html

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