IMO Shortlist 2010 problem G1


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23. lipnja 2013.
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Let ABC be an acute triangle with D, E, F the feet of the altitudes lying on BC, CA, AB respectively. One of the intersection points of the line EF and the circumcircle is P. The lines BP and DF meet at point Q. Prove that AP = AQ.

Proposed by Christopher Bradley, United Kingdom
Izvor: Međunarodna matematička olimpijada, shortlist 2010