[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/pBIRO6Gf.jpg

If six points are chosen, two points on each side of a triangle, such that they have the same ratio of distances to vertices, then the perpendicular lines through those points meet at six concyclic points. Has this been shown in the literature? If so, what is the formal name of this circle?