IMO Shortlist 2006 problem G6

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Dodao/la: arhiva
2. travnja 2012.
Circles w_{1} and w_{2} with centres O_{1} and O_{2} are externally tangent at point D and internally tangent to a circle w at points E and F respectively. Line t is the common tangent of w_{1} and w_{2} at D. Let AB be the diameter of w perpendicular to t, so that A, E, O_{1} are on the same side of t. Prove that lines AO_{1}, BO_{2}, EF and t are concurrent.
Izvor: Međunarodna matematička olimpijada, shortlist 2006