2021-22 Winter Team #10
Source:
April 17, 2022
geometry
Problem Statement
In triangle , let be the circumcenter. The incircle of is tangent to , and at points , and , respectively. Let be the centroid of triangle . Suppose the inradius and circumradius of is and , respectively. Over all such triangles , pick one that maximizes the area of triangle . If we write for relatively prime positive integers and , then find .