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.
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.