Problem B. 4743. (November 2015)
B. 4743. The inscribed circle of triangle \(\displaystyle ABC\) touches sides \(\displaystyle BC\), \(\displaystyle AC\) and \(\displaystyle AB\) at points \(\displaystyle A_1\), \(\displaystyle B_1\) and \(\displaystyle C_1\), respectively. Let the orthocentres of triangles \(\displaystyle AC_1B_1\), \(\displaystyle BA_1C_1\) and \(\displaystyle CB_1A_1\) be \(\displaystyle M_A\), \(\displaystyle M_B\) and \(\displaystyle M_C\), respectively. Show that triangle \(\displaystyle A_1B_1C_1\) is congruent to triangle \(\displaystyle M_AM_BM_C\).
Proposed by Sz. Miklós, Herceghalom
(4 pont)
Deadline expired on December 10, 2015.
Statistics:
112 students sent a solution.  
4 points:  88 students. 
3 points:  14 students. 
2 points:  4 students. 
1 point:  3 students. 
Unfair, not evaluated:  2 solutions. 
Unfair, not evaluated:  1 solution. 
