Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 667. (March 2016)

A. 667. On the circumcircle of the scalene triangle $\displaystyle ABC$, let $\displaystyle A_0$, $\displaystyle B_0$, and $\displaystyle C_0$ be the midpoints of the arcs $\displaystyle BAC$, $\displaystyle CBA$ and $\displaystyle ACB$, respectively. Denote by $\displaystyle A_1$, $\displaystyle B_1$ and $\displaystyle C_1$ the Feuerbach points of the triangles $\displaystyle AB_0C_0$, $\displaystyle BC_0A_0$ and $\displaystyle CA_0B_0$, respectively. Show that the triangles $\displaystyle A_0B_0C_0$ and $\displaystyle A_1B_1C_1$ are similar.

Russian problem

(5 pont)

Deadline expired on April 11, 2016.

### Statistics:

 6 students sent a solution. 4 points: Cseh Kristóf, Gáspár Attila, Glasznova Maja, Imolay András, Kovács 162 Viktória, Williams Kada.

Problems in Mathematics of KöMaL, March 2016