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
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.