Problem A. 530. (March 2011)
A. 530. There are given 2n+1 points (n2) lying on a circle in this order such that . The lines split the line segment A1A2n+1 into 2n-1 part; denote their lengths by , respectively. Prove that .
(Proposed by Zoltán Gyenes, Budapest)
Deadline expired on April 11, 2011.
12 students sent a solution. 5 points: Backhausz Tibor, Damásdi Gábor, Frankl Nóra, Gyarmati Máté, Janzer Olivér, Lenger Dániel, Mester Márton, Nagy 235 János, Nagy 648 Donát, Strenner Péter, Szabó 928 Attila. 2 points: 1 student.