IMO Shortlist 2000 problem G2

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Dodao/la: arhiva
2. travnja 2012.
Two circles G_1 and G_2 intersect at two points M and N. Let AB be the line tangent to these circles at A and B, respectively, so that M lies closer to AB than N. Let CD be the line parallel to AB and passing through the point M, with C on G_1 and D on G_2. Lines AC and BD meet at E; lines AN and CD meet at P; lines BN and CD meet at Q. Show that EP = EQ.
Izvor: Međunarodna matematička olimpijada, shortlist 2000