IMO Shortlist 2003 problem G5


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2. travnja 2012.
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Let ABC be an isosceles triangle with AC=BC, whose incentre is I. Let P be a point on the circumcircle of the triangle AIB lying inside the triangle ABC. The lines through P parallel to CA and CB meet AB at D and E, respectively. The line through P parallel to AB meets CA and CB at F and G, respectively. Prove that the lines DF and EG intersect on the circumcircle of the triangle ABC.

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(According to my team leader, last year some of the countries wanted a geometry question that was even easier than this...that explains IMO 2003/4...)

[Note by Darij: This was also Problem 6 of the German pre-TST 2004, written in December 03.]

Edited by Orl.
Izvor: Međunarodna matematička olimpijada, shortlist 2003