A circle of radius s containing all three points [Czech-Polish-Slovak 2018]
Source: Czech-Polish-Slovak Match 2018, Problem 4
July 2, 2018
Geometric Inequalitiesgeometryinequalities
Problem Statement
Let be an acute triangle with the perimeter of . We are given three pairwise disjoint circles with pairwise disjoint interiors with the centers , and , respectively. Prove that there exists a circle with the radius of which contains all the three circles. Proposed by Josef Tkadlec, Czechia