Mathematical and Physical Journal
for High Schools
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Problem A. 485. (September 2009)

A. 485. Let ABCD be a tetrahedron with circumcenter O. Suppose that the points P, Q and R are interior points of the edges AB, AC and AD, respectively. Let K, L, M and N be the centroids of the triangles PQD, PRC, QRB and PQR, respectively. Prove that if the plane PQR is tangent to the sphere KLMN then OP=OQ=OR.

(5 pont)

Deadline expired on November 10, 2009.


6 students sent a solution.
5 points:Éles András, Frankl Nóra, Nagy 235 János, Nagy 648 Donát, Szabó 928 Attila.
4 points:Weisz Ágoston.

Problems in Mathematics of KöMaL, September 2009