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. geometrygeometric transformationreflectionangle bisector