IMC 2004 — Keystage 3 (IWYMIC) — individual Question 15

In triangle $ABC$, $BC=a$ cm, $CA=b$ cm, $AB=c$ cm. Points $D,E,F$ lie on $BC,CA,AB$ respectively, with $DE\perp CA$ and $DF\perp AB$. Let $P=BE\cap CF$. If $AP\perp BC$, determine $BD$ in terms of $a,b,c$.