Take any point P and construct its pedal triangle by dropping perpendiculars to the sides of the triangle and[br]constructing a triangle using the feet of these perpendiculars (DEF)[br][br]"Pivot" these perpendiculars around P. Where these pivoted perpendiculars intersect the sides of the [br]triangle construct a new triangle using these points as the vertices (GHI)[br][br]This new triangle is always similar to the original pedal triangle. (Drag point G)