IMO Shortlist 1974 problem 5

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Dodao/la: arhiva
2. travnja 2012.
Let A_r,B_r, C_r be points on the circumference of a given circle S. From the triangle A_rB_rC_r, called \Delta_r, the triangle \Delta_{r+1} is obtained by constructing the points A_{r+1},B_{r+1}, C_{r+1}on S such that A_{r+1}A_r is parallel to B_rC_r, B_{r+1}B_r is parallel to C_rA_r, and C_{r+1}C_r is parallel to A_rB_r. Each angle of \Delta_1 is an integer number of degrees and those integers are not multiples of 45. Prove that at least two of the triangles \Delta_1,\Delta_2, \ldots ,\Delta_{15} are congruent.
Izvor: Međunarodna matematička olimpijada, shortlist 1974