**B. 4088.** *P* is an interior point of side *B*_{1}*B*_{2} of an acute-angled triangle *AB*_{1}*B*_{2}. Let *Q *denote the reflection of *P* about point *A*. Let *D*_{i} denote the perpendicular projection of *P* onto the line segment *AB*_{i}, and let *F*_{i} be the midpoint of the line segment *D*_{i}*B*_{i}. Prove that if *QD*_{1} is perpendicular to *PF*_{1}, then *QD*_{2} is perpendicular to *PF*_{2}.

Suggested by *J. Bodnár,* Budapest

(5 points)