Problem

Source: Romanian JBTST IV 2007, problem 2

Tags: geometry, power of a point, radical axis, geometry proposed



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 GDEAB, and H the symetric point of F w.r.t G. Find HCF.