Question 10
Let $ABCD$ be a convex quadrilateral, and let $N$ be the midpoint of $BC$. Suppose further that $\angle AND = 135^\circ$. Prove that
$$
|AB| + |CD| + \frac{1}{\sqrt{2}} \cdot |BC| \geqslant |AD|
$$
$$
|AB| + |CD| + \frac{1}{\sqrt{2}} \cdot |BC| \geqslant |AD|
$$