A. 373. P is a point in the interior of the quadrilateral A1A2A3A4 that does not lie on either diagonal. The points Bi lie in the interior of each line segment AiP. Let Cij be the intersection of the lines AiBj and AjBi (1i<j 4). Prove that the line segments C12C34, C13C24, C14C23 are all concurrent.
Deadline expired on 17 May 2005.