Question 14
Consider the points $O = (0,0)$, $A = (-2,0)$ and $B = (0,2)$ in the coordinate plane. Let $E$ and $F$ be the midpoints of $OA$ and $OB$ respectively. Rotate triangle $OEF$ clockwise about $O$ to reach a triangle $OE'F'$ and, for each rotated position, let $P = (x, y)$ be the intersection of lines $AE'$ and $BF'$. Find the maximum of the $y$-coordinate of $P$.