Here is a cute geometry problem I saw some time ago. I know the solution, I just wanted to share ;-) (Please, don't be mad at me.)
Consider an acute triangle △ABC. Let AP, AQ and BP,BQ be the angle trisectors as shown on the picture below. Prove that |∠APQ|=|∠QPB|.
Edit: There does exist one very simple and elegant solution, so don't be stumbled if you happen to guess/derive it.
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