Mathematical and Physical Journal
for High Schools
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Problem A. 413. (December 2006)

A. 413. Let O be the point of intersection of the diagonals AC, BD of a convex quadrilateral ABCD. Let G1 and G2 be the centroids of triangles OAB and OCD, respectively. Let H1 and H2 be the orthocenters of triangles OBC and ODA, respectively. Prove that G1G2 is perpendicular to H1H2.

(Vietnamese competitoon problem)

(5 pont)

Deadline expired on January 15, 2007.


Statistics:

17 students sent a solution.
5 points:Blázsik Zoltán, Bogár 560 Péter, Dobribán Edgár, Fischer Richárd, Fridrik József Richárd, Gyenizse Gergő, Győrffy Lajos, Hujter Bálint, Kisfaludi-Bak Sándor, Kónya 495 Gábor, Korándi Dániel, Kutas Péter, Lovász László Miklós, Nagy 224 Csaba, Nagy 235 János, Nagy 314 Dániel, Tomon István.

Problems in Mathematics of KöMaL, December 2006