AT-OEMO-REG 2009 Problem 3

Let $D$ , $E$ , $F$ be the feet of the altitudes wrt sides $BC$ , $CA$ , $AB$ of acute-angled triangle $\triangle ABC$ , respectively. In triangle $\triangle CFB$ , let $P$ be the foot of the altitude wrt side $BC$ . Define $Q$ and $R$ wrt triangles $\triangle ADC$ and $\triangle BEA$ analogously. Prove that lines $AP$ , $BQ$ , $CR$ don't intersect in one common point.