Question 23
In the diagram below, $ABC$ is an isosceles triangle with $|AC|=|BC|$. The point $D$ lies on $AC$ such that $BD$ is perpendicular to $AC$. The point $E$ lies on $BC$ such that $DE$ is parallel to $AB$. If $|AD|=3$, $|AB|=5$ and $$\frac{\text{Area }\triangle CDE}{\text{Area }\triangle CAB}=\frac mn,$$ where $m$ and $n$ are positive integers with no common factor larger than 1, find the value of $m+n$.
