Mathematical and Physical Journal
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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.


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