We consider triangles $ABC$, in which the point $M$ lies on the side $AB$, $AM = a$, $BM = b$, $CM = c$ ($c <a, c <b$). Find the smallest radius of the circumcircle of such triangles.
Problem
Source: 2017 Oral Moscow Geometry Olympiad grades 8-9 p4
Tags: geometry, circumcircle, circumradius, radius, minimum value