28-Six Concyclic Points via Antipedal Triangle

Let  be a triangle, and  be any point on the plane.  respectively are three lines perpendicular with  at .  meets  at ,  meets  at ,  meets  at . Circle center , radii  meet  at . Define  and  cyclically. Prove that six points  lie on a circle.

http://www.cut-the-knot.org/m/Geometry/SixConcyclicPoints.shtml