Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 695. (April 2017)

A. 695. We are given $\displaystyle 2k$ lines, $\displaystyle e_1, \ldots, e_{2k}$ in a plane $\displaystyle S$, further given a line $\displaystyle g$ which has an angle $\displaystyle \alpha$ with $\displaystyle S$. Show that the sum of the pairwise angles between the lines $\displaystyle e_1, \ldots,e_{2k}, g$ is at most

$\displaystyle (k^2+k)\cdot \dfrac \pi 2 + k\alpha.$

(5 pont)

Deadline expired on May 10, 2017.

### Statistics:

 9 students sent a solution. 5 points: Baran Zsuzsanna, Gáspár Attila, Imolay András, Matolcsi Dávid, Szabó Kristóf, Williams Kada. 4 points: Schrettner Jakab. 3 points: 1 student. 0 point: 1 student.

Problems in Mathematics of KöMaL, April 2017