RO-NMO 2007 Problem 72

Consider the triangle $ABC$ with $m(\angle BAC = 90^\circ)$ and $AC = 2AB$ . Let $P$ and $Q$ be the midpoints of $AB$ and $AC$ ,respectively. Let $M$ and $N$ be two points found on the side $BC$ such that $CM = BN = x$ . It is also known that $2S[MNPQ] = S[ABC]$ . Determine $x$ in function of $AB$ .