circle tangent to the incircle criterion using radius of excircle
Source: 2017 Oral Moscow Geometry Olympiad grades 10-11 p4
July 25, 2019
geometryincircleexcircleexradiustangent circles
Problem Statement
Prove that a circle constructed with the side of a triangle as a diameter touches the inscribed circle of the triangle if and only if the side is equal to the radius of the exircle on that side.