Question 5
Choose distinct points $C,D$ on segment $AB$ with $C$ between $A$ and $D$. Construct squares $ACMN$, $ADGH$, $BCPQ$ and $BDEF$ so that $M,P$ lie in one half-plane bounded by line $AB$, while $G,E$ lie in the other. Let $I$ be the intersection of $QH$ and $FN$. Prove that $IC=ID$.
