KöMaL 2016 K497

In a right-angled triangle $ABC$ , $BC = 5$ and $AB = 12$. $M$ is the intersection of hypotenuse $AC$ with the arc of radius $AB$ centred at $A$ , and $N$ is the intersection of hypotenuse $AC$ with the arc $BC$ centred at $C$ . Determine the distance between points $M$ and $N$ .