Question 27
A quadrilateral $A B C D$ with right angles at the vertices $A$ and $C$ is given. The orthogonal projections of the vertices $D$ and $B$ onto the segment $A C$ are denoted by $E$ and $F$, respectively. What is the length of the segment $B F$ if $|A E|=3, |D E|=5$ and $|C E|=7$?