IMO Shortlist 2004 problem G5

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Dodao/la: arhiva
2. travnja 2012.
Let A_1A_2A_3...A_n be a regular n-gon. Let B_1 and B_n be the midpoints of its sides A_1A_2 and A_{n-1}A_n. Also, for every i\in\left\{2;\;3;\;4;\;...;\;n-1\right\}, let S be the point of intersection of the lines A_1A_{i+1} and A_nA_i, and let B_i be the point of intersection of the angle bisector bisector of the angle \measuredangle A_iSA_{i+1} with the segment A_iA_{i+1}.

Prove that: \sum_{i=1}^{n-1} \measuredangle A_1B_iA_n=180^{\circ}.
Izvor: Međunarodna matematička olimpijada, shortlist 2004