Mathematical and Physical Journal
for High Schools
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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