Problem 1.
  Let ABC be an acute-angled triangle with AC>AB  and let D be the foot of the A -angle bisector on BC. The reflections of lines AB and AC in line BC meet AC and AB at points E and F respectively. A line through D meets AC and AB at G and H respectively such that G lies strictly between A and C while H lies strictly between B and F. Prove that the circumcircles of △EDG and △FDH are tangent to each other.