Question 8
Given a triangle $ABC$ with $m(\angle A) = 90^\circ$, $AC \lt AB$, consider on the rays $BA$ and $AC$ points $E$ and $D$ respectively, such that $A \in (BE)$, $C \in (AD)$, $AE = AC$ and $AD = AB$. Denote by $M$ and $N$ the midpoints of $[BC]$ and $[DE]$ respectively, and let $\{R\} = EC \cap BD$. Show that $MN = RA$.