2001 USAMO Problems/Problem 6

Problem

Each point in the plane is assigned a real number such that, for any triangle, the number at the center of its inscribed circle is equal to the arithmetic mean of the three numbers at its vertices. Prove that all points in the plane are assigned the same number.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

2001 USAMO (Problems • Resources)
Preceded by Problem 5	Followed by Last question
1 • 2 • 3 • 4 • 5 • 6
All USAMO Problems and Solutions