IMO Shortlist 1983 problem 23

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Dodao/la: arhiva
2. travnja 2012.
Let A be one of the two distinct points of intersection of two unequal coplanar circles C_1 and C_2 with centers O_1 and O_2 respectively. One of the common tangents to the circles touches C_1 at P_1 and C_2 at P_2, while the other touches C_1 at Q_1 and C_2 at Q_2. Let M_1 be the midpoint of P_1Q_1 and M_2 the midpoint of P_2Q_2. Prove that \angle O_1AO_2=\angle M_1AM_2.
Izvor: Međunarodna matematička olimpijada, shortlist 1983