Stage Senior, problemi noti: G3
In this video, we'll solve problem 2 of the 2009 Balkan Mathematical Olympiad, a problem with many different solutions, including a trigonometric one, a complex one, and a circular inversion one. The solution I propose is purely synthetic and requires, as an advanced tool, only knowledge of one property of the simmedian. Sources for further study of the simmedian theorem: Euclidean Geometry in Mathematical Olympiads, by Evan Chen. This book (also available in PDF format) is one of the most famous and comprehensive geometry resources for the Mathematical Olympiads. Problem solving in geometry, by Carlo Cassola, U Math series. "Let's Talk About Symmedians!" by Sammy Luo and Cosmin Pohoata. A short paper easily found online that presents this theorem (and many others) with a proof. 0:00 - Introduction 1:31 - AP median 3:39 - Simmedian AQ 6:27 - MBQ similar to NCQ 8:11 - Angle chasing
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