MathNet 2007-part-03 — 185 problems (EN–VI) Question 124

$A$, $B$, $C$, and $D$ are points on a circle, and segments $\overline{AC}$ and $\overline{BD}$ intersect at $P$, such that $AP = 8$, $PC = 1$, and $BD = 6$. Find $BP$, given that $BP \lt DP$.