4 points are centers of circles, 3 pairwise externally tangent, 3 tangent to 4th
Source: Sharygin 2013 Final 8.7
August 16, 2018
geometrycirclesrectangle
Problem Statement
In the plane, four points are marked. It is known that these points are the centers of four circles, three of which are pairwise externally tangent, and all these three are internally tangent to the fourth one. It turns out, however, that it is impossible to determine which of the marked points is the center of the fourth (the largest) circle. Prove that these four points are the vertices of a rectangle.