TOPICS
Search

Parry Reflection Point


ParryReflectionPoint

The Parry reflection point is the triangle center where three reflected lines concur. Draw lines through the vertices A, B, and C of a triangle parallel to its Euler line, then reflect them in the opposite sidelines BC, CA, and AB, respectively. It is Kimberling center X_(399) and has triangle center function

 alpha_(399)=-8sinBsinCcos^2A+5cosA-4cosBcosC.

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

Explore with Wolfram|Alpha

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.

Referenced on Wolfram|Alpha

Parry Reflection Point

Cite this as:

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

Subject classifications