Australian AMC 2024 - Intermediate Question 18

Question 18

Triangle $ABC$ has a right angle at $A$, and side $AC$ is twice as long as $AB$. Also $MN$ is the perpendicular bisector of $BC$, as shown. In area, what fraction of $\triangle ABC$ is $\triangle CMN$?

Question illustration

$\frac13$
$\frac1{\sqrt5}$
$\frac25$
$\frac{\sqrt5}{8}$
$\frac5{16}$