Question 97
Let $ABCD$ be a unit square (that is, the labels $A$, $B$, $C$, $D$ appear in that order around the square). Let $X$ be a point outside of the square such that the distance from $X$ to $AC$ is equal to the distance from $X$ to $BD$, and also that $AX = \frac{\sqrt{2}}{2}$. Determine the value of $CX^{2}$.
