MathDB
IMO Shortlist 2010 - Problem G1

Source:

July 17, 2011
geometrycircumcirclegeometric transformationreflectionIMO Shortlist

Problem Statement

Let ABCABC be an acute triangle with D,E,FD, E, F the feet of the altitudes lying on BC,CA,ABBC, CA, AB respectively. One of the intersection points of the line EFEF and the circumcircle is P.P. The lines BPBP and DFDF meet at point Q.Q. Prove that AP=AQ.AP = AQ.
Proposed by Christopher Bradley, United Kingdom
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