Problem A. 488. (October 2009)
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 November 10, 2009.
8 students sent a solution. 5 points: Bodor Bertalan, Éles András, Frankl Nóra, Márkus Bence, Nagy 235 János, Nagy 648 Donát, Szabó 928 Attila. 2 points: 1 student.