Summary
In geometry, the equal parallelians point[1][2] (also called congruent parallelians point) is a special point associated with a plane triangle. It is a triangle center and it is denoted by X(192) in Clark Kimberling's Encyclopedia of Triangle Centers.[3] There is a reference to this point in one of Peter Yff's notebooks, written in 1961.[1]
Definition edit
The equal parallelians point of triangle △ABC is a point P in the plane of △ABC such that the three line segments through P parallel to the sidelines of △ABC and having endpoints on these sidelines have equal lengths.[1]
Trilinear coordinates edit
The trilinear coordinates of the equal parallelians point of triangle △ABC are
Construction for the equal parallelians point edit
Let △A'B'C' be the anticomplementary triangle of triangle △ABC. Let the internal bisectors of the angles at the vertices A, B, C of △ABC meet the opposite sidelines at A", B", C" respectively. Then the lines A'A", B'B", C'C" concur at the equal parallelians point of △ABC.[2]
See also edit
References edit
- ^ a b c Kimberling, Clark. "Equal Parallelians Point". Archived from the original on 16 May 2012. Retrieved 12 June 2012.
- ^ a b Weisstein, Eric. "Equal Parallelians Point". MathWorld--A Wolfram Web Resource. Retrieved 12 June 2012.
- ^ Kimberling, Clark. "Encyclopedia of Triangle Centers". Archived from the original on 19 April 2012. Retrieved 12 June 2012.