Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 401. (May 2006)

A. 401. ABCD is a tetrahedron. The insphere touches the face ABC at H. The exsphere opposite D (which also touches the face ABC and the three planes containing the other faces) touches the face ABC at O. If O is the circumcenter of ABC, show that H is the orthocenter of ABC.

Polish competition problem

(5 pont)

Deadline expired on June 15, 2006.


7 students sent a solution.
5 points:Erdélyi Márton, Hujter Bálint, Jankó Zsuzsanna, Kisfaludi-Bak Sándor, Nagy 224 Csaba, Paulin Roland, Tomon István.

Problems in Mathematics of KöMaL, May 2006