5 triangles, for any 2, distance between 2 triangles = sum of their circumradii
Source: 2021 Sharygin Finals grade IX p4
August 1, 2021
circumradiusdistancegeometrycombinatorial geometry
Problem Statement
Define the distance between two triangles to be the closest distance between two vertices, one from each triangle. Is it possible to draw five triangles in the plane such that for any two of them, their distance equals the sum of their circumradii?