Equal parallelians point

[3] There is a reference to this point in one of Peter Yff's notebooks, written in 1961.

[1] 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] The trilinear coordinates of the equal parallelians point of triangle △ABC are

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.

Reference triangle △ ABC
Line segments of equal length, parallel to the sidelines of △ ABC
Construction of the equal parallelians point.
Reference triangle △ ABC
Internal bisectors of △ ABC (intersect opposite sides at A", B", C" )
Anticomplementary triangle △ A'B'C' of △ ABC
Lines ( A'A", B'B", C'C" ) concurrent at the equal parallelians point