With the circle geometry question, for ii;
\dpi{120} \angle EAC (\dpi{120} \angle BAC) is a fixed angle as it lies on the fixed chord BC.
Therefore in triangle AEC, \dpi{120} \angle AEC and \dpi{120} \angle EAC are constants, thus \dpi{120} \angle ACE is a constant angle.
Since the constant...