Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# 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