Let ABC be a triangle such that AB<AC<BC. Let D,E be points on the segment BC such that BD=BA and CE=CA. If K is the circumcenter of triangle ADE, F is the intersection of lines AD,KC and G is the intersection of lines AE,KB, then prove that the circumcircle of triangle KDE (let it be c1), the circle with center the point F and radius FE (let it be c2) and the circle with center G and radius GD (let it be c3) concur on a point which lies on the line AK. geometrycircumcircleconcurrency