Mathematical and Physical Journal
for High Schools
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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.

### 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