Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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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 t_i and O_i the area and the circumcenter of the triangle QP_i+1P_i+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

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.