2014 IMO Problems/Problem 4

Problem

Points $P$ and $Q$ lie on side $BC$ of acute-angled $\triangle{ABC}$ so that $\angle{PAB}=\angle{BCA}$ and $\angle{CAQ}=\angle{ABC}$ . Points $M$ and $N$ lie on lines $AP$ and $AQ$ , respectively, such that $P$ is the midpoint of $AM$ , and $Q$ is the midpoint of $AN$ . Prove that lines $BM$ and $CN$ intersect on the circumcircle of $\triangle{ABC}$ .

Solution

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.

2014 IMO (Problems) • Resources
Preceded by Problem 3	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 5
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2014 IMO Problems/Problem 4

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