Question 42
Points $A$, $B$, $C$, $D$ lie on a circle in this order, where $AB$ and $CD$ are not parallel. The length of the arc $\widehat{AB}$ that contains points $C$, $D$ is twice as large as the length of the arc $\widehat{CD}$ that does not contain points $A$, $B$. Point $E$ is chosen such that $AC = AE$ and $BD = BE$ and $E$ lies on the same side of the line $AB$ as $C$ and $D$. Assuming that the perpendicular line from the point $E$ to the line $AB$ bisects the arc $\widehat{CD}$ not containing points $A$, $B$, prove that $\angle ACB = 108^\circ$.