Home > Geometry, IMO, Olympiad > IMO 2014 Problem 4

IMO 2014 Problem 4


Let {P} and {Q} be on segment {BC} of an acute triangle {ABC} such that {\angle PAB=\angle BCA} and {\angle CAQ=\angle ABC}. Let {M} and {N} be the points on {AP} and {AQ}, respectively, such that {P} is the midpoint of {AM} and {Q} is the midpoint of {AN}. Prove that the intersection of {BM} and {CN} is on the circumference of triangle {ABC}.

IMO 2014 Problem 4 (Day 2)

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Categories: Geometry, IMO, Olympiad Tags: ,
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