Question 72
The points $D$ and $E$ lie respectively on the perpendicular bisectors of the sides $AB$ and $BC$ of $\triangle ABC$. It is known that $D$ is an interior point for $\triangle ABC$, $E$ does not and $\measuredangle ADB = \measuredangle CEB$. If the line $AE$ meets the segment $CD$ at a point $O$, prove that the areas of $\triangle ACO$ and the quadrilateral $DBEO$ are equal.