Problem

Source: Czech and Slovak Olympiad 2016, National Round, III A p2

Tags: exradius, inradius, right triangle, geometry



Let us denote successively $r$ and $r_a$ the radii of the inscribed circle and the exscribed circle wrt to side BC of triangle $ABC$. Prove that if it is true that $r+r_a=|BC|$ , then the triangle $ABC$ is a right one