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## 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)