Barycentric coordinates in olympiad geometry. A follow-up to Chapter 7 of EGMO.
Unit Summary
Barycentric coordinates are one of the most effective bash techniques in geometry. This unit provides some standard applications of barycentric coordinates, building off of the prerequisite reading, Evan Chen’s barycentric coordinate handout. You will learn to use several standard formulae, and combine them with synthetic observations to solve difficult problems.
The B version is quite difficult for a B unit, but is still certainly achievable for someone with limited exposure to barycentrics. It has 54 clubs across 16 problems; it is a fairly small unit.
After this unit, some good units to try are Complex Numbers, Super Bary, Elem Geo, Art School, amongst other standard geometry units.
Warning
Important: DO NOT ABUSE BARYCENTRICS! Bash is always the last resort technique, and your overall development as a geometer will lack if you overuse barycentrics. Furthermore, do not “mark off” problems if you solve them via barycentrics, especially those before 2015. Problem writers were(and still somewhat are) largely unaware if their problems are destroyed by barycentrics, so even if a problem has an extremely easy barycentric solution, it is better to solve it synthetically.
Notable Problems
2014 IMO 4: Cute, short, simple, and sweet.
2015 SL G4: Fight this beast with your guns.