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 15 June 2006.