IMO Shortlist 2006 problem G5


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In triangle ABC, let J be the center of the excircle tangent to side BC at A_{1} and to the extensions of the sides AC and AB at B_{1} and C_{1} respectively. Suppose that the lines A_{1}B_{1} and AB are perpendicular and intersect at D. Let E be the foot of the perpendicular from C_{1} to line DJ. Determine the angles \angle{BEA_{1}} and \angle{AEB_{1}}.
Izvor: Međunarodna matematička olimpijada, shortlist 2006