You are given an arbitrary triangle ABC. Inside ABC there is a point M such that Area(ABM) = Area(BCM) = Area(ACM) . Prove that M is the centroid of triangle ABC. I have had very little progress with this question. I've tried connecting a line from M which bisects BC, but I cannot prove that the two lines are collinear. I've also tried continuing on AM until it intersects BC., but I cannot prove it bisects BC. Does anyone have any ideas?