MathNet 2022-part-02 — 197 problems (EN–VI) Question 161

$ABCD$ is a square with side length $1$. $P$ and $Q$ are points on $AB$ and $BC$ respectively such that $BP = BQ = \frac{1}{\sqrt{2}}$. $N$ is the foot of perpendicular from $B$ to $CP$. Find $NQ^2$.