Geometry Problem 1382: Circle, Diameter, Radius, Perpendicular, Congruence

Proposition

The figure below shows a point P on a circle O and two diameters AB and CD. PE and PF are perpendicular to AB and CD, respectively. If CG is perpendicular to AB, prove that CG and EF are congruent.
 

Geometry Problem 1382: Circle, Diameter, Radius, Perpendicular, Congruence
 

See also
Conformal Mapping or Transformation of Problem 1382