**A. 373.** *P* is a point in the interior of the quadrilateral *A*_{1}*A*_{2}*A*_{3}*A*_{4} that does not lie on either diagonal. The points *B*_{i} lie in the interior of each line segment *A*_{i}*P*. Let *C*_{ij} be the intersection of the lines *A*_{i}*B*_{j} and *A*_{j}*B*_{i} (1*i*<*j* 4). Prove that the line segments *C*_{12}*C*_{34}, *C*_{13}*C*_{24}, *C*_{14}*C*_{23} are all concurrent.

(5 points)

**Deadline expired on 17 May 2005.**