Question 4
Let $ABC$ be a right triangle with $\hat{C} = 90^\circ$. Points $D$ and $E$ on the hypotenuse $AB$ are such that $AD = AC$ and $BE = BC$. Points $P$ and $Q$ on $AC$ and $BC$ respectively are such that $AP = AE$ and $BQ = BD$. Let $M$ be the midpoint of segment $PQ$. Find $\hat{AM}\hat{B}$.