Question 152
In the triangle $ABC$ the lengths of the sides are given: $|AB| = 15$ cm, $|BC| = 14$ cm and $|CA| = 13$ cm. Let $D$ be the foot of the altitude from $A$ and let $E$ be a point on this altitude such that $\angle BAD = \angle DEC$. Denote the intersection of lines $AB$ and $CE$ by $F$. Find $|EF|$.