5

Part of 2011 Japan MO Finals

Problems(1)

2011 Japan Mathematical Olympiad Finals Problem 5

Source: Japanese MO Finals 2011

Given 4 points on a plane. Suppose radii of 4 incircles of the triangles, which can be formed by any 3 points taken from the 4 points, are equal. Prove that all of the triangles are congruent.

geometryrectangleincenterparallelogramgeometry proposed