Question 26
Several small circles are arranged inside a unit circle $\Gamma$. The sum of the perimeters of all these small circles is not less than $\pi$ and none of them includes the center of $\Gamma$.
Prove that there exists a concentric with $\Gamma$ circumference intersecting at least two of these small circles.
Prove that there exists a concentric with $\Gamma$ circumference intersecting at least two of these small circles.