IMO Shortlist 2009 problem G1

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Dodao/la: arhiva
2. travnja 2012.
Let ABC be a triangle with AB = AC . The angle bisectors of \angle C AB and \angle AB C meet the sides B C and C A at D and E , respectively. Let K be the incentre of triangle ADC. Suppose that \angle B E K = 45^\circ . Find all possible values of \angle C AB .

Jan Vonk, Belgium, Peter Vandendriessche, Belgium and Hojoo Lee, Korea
Izvor: Međunarodna matematička olimpijada, shortlist 2009