Parry Reflection Point
ParryReflectionPoint
Let L, M, and N be lines through A, B, C, respectively, parallel to the Euler line. Let L^' be the reflection of L in sideline BC, let M^' be the reflection of M in sideline CA, and let N^' be the reflection of N in sideline AB. The lines L^', M^', and N^' then concur in a point known as the Parry reflection point, which is Kimberling center X_(399) and has triangle center function
| alpha_(399)=-8sinBsinCcos^2A+5cosA-4cosBcosC. |
See also
Euler Line, Parry Point, ReflectionExplore with Wolfram|Alpha
WolframAlpha
References
Kimberling, C. "Encyclopedia of Triangle Centers: X(399)=Parry Reflection Point." https://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X399.Parry, C. "Problem 10637." Amer. Math. Monthly 105, 68, 1998.Referenced on Wolfram|Alpha
Parry Reflection PointCite this as:
Weisstein, Eric W. "Parry Reflection Point." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ParryReflectionPoint.html