8.3

Part of 2004 All-Russian Olympiad Regional Round

Problems(1)

equilateral, median AM=d(M,AB)+d(M,AC) - All-Russian MO 2004 Regional (R4) 8.3

Source:

In an acute triangle, the distance from the midpoint of any side to the opposite vertex is equal to the sum of the distances from it to sides of the triangle. Prove that this triangle is equilateral.

geometryEquilateralmedian