Points, whose pedal triangles are similar to the given triangle
  We study the eleven points in the plane of a given triangle, whose pedal triangles are similar to the given one. We prove that the six points whose pedal triangles are positively oriented, lie on a single circle, while the five points, whose pedal triangles are negatively oriented, lie on a common straight line. 
Georgi Ganchev, Gyulbeyaz Ahmed and Marinella Petkova
math.HO