Question 75
In the interior of non-zero angle $\widehat{AOD}$ consider points $B$ and $C$ such that $OA = OB$, $OD = OC$, the segments $AC$ and $BD$ meet in $P$, and the semi-line $PO$ is the angle bisector of $\widehat{APD}$. Prove that the angles $\widehat{AOB}$ and $\widehat{COD}$ are equal.