Let w1 and w2 be two circles which intersect at points A and B. Consider w3 another circle which cuts w1 in D,E, and it is tangent to w2 in the point C, and also tangent to AB in F. Consider G∈DE∩AB, and H the symetric point of F w.r.t G. Find ∠HCF.
Problem
Source: Romanian JBTST IV 2007, problem 2
Tags: geometry, power of a point, radical axis, geometry proposed