Mathematical and Physical Journal
for High Schools
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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 t_1\cdot \overrightarrow{OO_1} + t_2\cdot \overrightarrow{OO_2} + t_3\cdot
\overrightarrow{OO_3} = 0.

(5 pont)

Deadline expired on November 10, 2009.


Statistics:

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.

Problems in Mathematics of KöMaL, October 2009