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. 4693. (February 2015)

B. 4693. \(\displaystyle K\) is a point on side \(\displaystyle AC\) of triangle \(\displaystyle ABC\) such that \(\displaystyle AK=2KC\) and \(\displaystyle \angle ABK = 2 \angle KBC\). Let \(\displaystyle F\) denote the midpoint of side \(\displaystyle AC\), and let \(\displaystyle L\) be the orthogonal projection of point \(\displaystyle A\) onto the line segment \(\displaystyle BK\). Prove that the lines \(\displaystyle FL\) and \(\displaystyle BC\) are perpendicular.

(5 pont)

Deadline expired on March 10, 2015.


Statistics:

34 students sent a solution.
5 points:Andi Gabriel Brojbeanu, Baran Zsuzsanna, Cseh Kristóf, Csépai András, Czirkos Angéla, Eper Miklós, Fekete Panna, Gáspár Attila, Geng Máté, Gyulai-Nagy Szuzina, Kerekes Anna, Keresztfalvi Bálint, Kocsis Júlia, Kovács 101 Dávid Péter, Leitereg Miklós, Mócsy Miklós, Nagy Kartal, Nagy-György Pál, Németh 123 Balázs, Polgár Márton, Porupsánszki István, Sal Kristóf, Schrettner Bálint, Schwarcz Tamás, Szebellédi Márton, Vághy Mihály, Varga-Umbrich Eszter, Várkonyi Dorka, Vu Mai Phuong, Wiandt Péter, Williams Kada.
2 points:3 students.

Problems in Mathematics of KöMaL, February 2015