I found this problem off of mathematics magazine and I want to give it a try solving it, but i'm lost for ideas. The problem states the following: Let G be the centroid of triangle ABC. Prove that if angle BAC = 60 degrees and angle BGC = 120 degrees then the triange is equilateral. My idea was to use the medians to find G and find the angles that way. I then quickly realized I assumed to many things, so now i'm asking for new outlooks on this problem. Perhaps i've been staring at it for far to long, but i'm stump. Any ideas?