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:
111 students sent a solution. 4 points: 88 students. 3 points: 14 students. 2 points: 4 students. 1 point: 3 students. Unfair, not evaluated: 2 solutionss.
Problems in Mathematics of KöMaL, November 2015