Question 179
On the unit square $ABCD$ the point $E$ on $CD$ is given in such a way that $|\angle BAE| = 60^\circ$. Further, let $X$ be an arbitrary interior point of the segment $AE$. Finally, let $Y$ be the intersection of the line perpendicular to $BX$ and containing $X$ with the line $BC$. What is the least possible length of $BY$? (Michal Rolínek)