Question 6
Each point in the plane is assigned a real number.
Suppose that for any nondegenerate triangle, the number at its incenter
is the arithmetic mean of the three numbers at its vertices.
Prove that all points in the plane were assigned the same number.
Suppose that for any nondegenerate triangle, the number at its incenter
is the arithmetic mean of the three numbers at its vertices.
Prove that all points in the plane were assigned the same number.