Mathematical and Physical Journal
for High Schools
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Problem B. 4749. (November 2015)

B. 4749. The feet of the altitudes drawn from vertices \(\displaystyle B\) and \(\displaystyle C\) of an acute-angled triangle \(\displaystyle ABC\) on the sides \(\displaystyle AC\) and \(\displaystyle AB\) are \(\displaystyle D\) and \(\displaystyle E\), respectively. The midpoint of side \(\displaystyle BC\) is \(\displaystyle F\). The intersection of line segments \(\displaystyle AF\) and \(\displaystyle DE\) is \(\displaystyle M\), and the orthogonal projection of point \(\displaystyle M\) onto the line segment \(\displaystyle BC\) is \(\displaystyle N\). Prove that line segment \(\displaystyle AN\) bisects line segment \(\displaystyle DE\).

Proposed by B. Bíró, Eger - In memoriam Attila Kálmán

(6 pont)

Deadline expired on December 10, 2015.


Statistics:

36 students sent a solution.
6 points:Barabás Ábel, Baran Zsuzsanna, Bodolai Előd, Bukva Balázs, Cseh Kristóf, Csorba Benjámin, Czirkos Angéla, Gáspár Attila, Hansel Soma, Horváth András János, Imolay András, Kerekes Anna, Keresztfalvi Bálint, Kocsis Júlia, Kovács 162 Viktória, Lajkó Kálmán, Lakatos Ádám, Molnár-Sáska Zoltán, Nagy Dávid Paszkál, Németh 123 Balázs, Polgár Márton, Radnai Bálint, Schrettner Bálint, Stein Ármin, Vághy Mihály, Vankó Miléna, Varga-Umbrich Eszter.
5 points:Andó Angelika, Döbröntei Dávid Bence, Matolcsi Dávid.
4 points:1 student.
3 points:2 students.
2 points:1 student.
1 point:1 student.
0 point:1 student.

Problems in Mathematics of KöMaL, November 2015