A. 488. Let P1P2P3 be a triangle with circumcenter O, the point Q is in the triangle. Denote ti and Oi the area and the circumcenter of the triangle QPi+1Pi+2, respectively, where i=1,2,3 (the vertices are counted cyclically: P4=P1 and P5=P2). Prove that .
Deadline expired on 10 November 2009.