2011 Japan Mathematical Olympiad Finals Problem 5
Source: Japanese MO Finals 2011
February 11, 2011
geometryrectangleincenterparallelogramgeometry proposed
Problem Statement
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.