Let ABCD be a cyclic quadrilaterla and let E be the point of intersection of its diagonals AC and BD. Suppose AD and BC meet in F. Let the midpoints of AB and CD be G and H respectively. If Γ is the circumcircle of triangle EGH, prove that FE is tangent to Γ. geometrycircumcirclegeometric transformationdilationreflectionparallelogramangle bisector