Let ABC be a triangle inscribed in circle (I) that is tangent to the sides BC,CA,AB at points D,E,F respectively. Assume that L is the intersection of BE and CF,G is the centroid of triangle DEF,K is the symmetric point of L about G. If DK meets EF at P,Q is on EF such that QF=PE, prove that ∠DGE+∠FGQ=180o.Nguyễn Minh Hà incirclegeometryanglesequal segments