CAPS 2018 Problem 4

Let $ABC$ be an acute triangle with the perimeter of $2s$ . We are given three pairwise disjoint circles with pairwise disjoint interiors with the centers $A, B$ , and $C$ , respectively. Prove that there exists a circle with the radius of $s$ which contains all the three circles.

Proposed by Josef Tkadlec, Czechia