equal circles
Source: IVSoros Olympiad 1997-98 Corr. 10.10 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
June 1, 2024
geometryequal circles
Problem Statement
A circle touches the extensions of sides and of triangle , and also touches side of this triangle at point . Prove that the radius of the circle tangent to segments , and the circumscribed circle of this triangle is equal to the radius of the inscribed circle in this triangle.