Question 188
$P$ is a point inside triangle $ABC$, and lines $AP$, $BP$, $CP$ intersect the opposite sides $BC$, $CA$, $AB$ in points $D$, $E$, $F$, respectively. It is given that $\angle APB = 90^{\circ}$, and that $AC = BC$ and $AB = BD$. We also know that $BF = 1$, and that $BC = 999$. Find $AF$.
