Question 48
Let $AB$ and $CD$ be chords in a circle of center $O$ with $A, B, C, D$ distinct, and let the lines $AB$ and $CD$ meet at a right angle at point $E$. Let also $M$ and $N$ be the midpoints of $AC$ and $BD$ respectively. If $MN \perp OE$, prove that $AD \parallel BC$.