Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?
I want the old design back!!! :-)

Problem B. 4791. (April 2016)

B. 4791. Altitudes \(\displaystyle AD\) and \(\displaystyle CE\) of triangle \(\displaystyle ABC\) intersect at point \(\displaystyle M\). Line \(\displaystyle DE\) intersects the line of side \(\displaystyle AC\) at \(\displaystyle P\). Prove that line \(\displaystyle PM\) is perpendicular to the median drawn from vertex \(\displaystyle B\) of the triangle.

(Kvant)

(5 pont)

Deadline expired on May 10, 2016.


Statistics:

48 students sent a solution.
5 points:Andó Angelika, Cseh Kristóf, Csorba Benjámin, Fuisz Gábor, Horváth András János, Kocsis Júlia, Kondákor Márk, Nagy Dávid Paszkál, Polgár Márton, Szabó 417 Dávid, Vágó Ákos, Váli Benedek.
4 points:Baran Zsuzsanna, Bodolai Előd, Döbröntei Dávid Bence, Gáspár Attila, Hansel Soma, Imolay András, Kerekes Anna, Kovács 711 Bálint, Lajkó Kálmán, Lakatos Ádám, Matolcsi Dávid, Molnár-Sáska Zoltán, Németh 123 Balázs, Schrettner Bálint, Szabó Kristóf, Szemerédi Levente, Varsányi András.
3 points:10 students.
2 points:3 students.
1 point:2 students.
0 point:3 students.
Unfair, not evaluated:1 solution.

Problems in Mathematics of KöMaL, April 2016