VMO 1991 Problem 5
The triangle ABC has centroid G. The lines GA, GB, GC meet the circumcircle again at D, E, F. Show that 3/R ≤ 1/GD + 1/GE + 1/GF ≤ √3 (1/AB + 1/BC + 1/CA), where R is the circumradius.
Community text Kalva (prase.cz mirror). Quoted with source.
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