Question 22
The side lengths of a triangle $ABC$ are given: $|AB| = 15~\mathrm{cm}$, $|BC| = 14~\mathrm{cm}$ and $|CA| = 13~\mathrm{cm}$. Let $D$ be the foot of the altitude to the side $BC$, and let $E$ be a point on this altitude such that $\angle BAD = \angle DEC$. Denote the intersection of the lines $AB$ and $CE$ by $F$. Calculate $|EF|$.