The Problem is:
Prove that one circle contains the other circle's radius when six circles meet at one point in a plane.
Comment:
This problem is one of exercises in my textbook on chapter pigeonhole principle. To get some hint, I tried drawing identical circles one by one and I could get it by picture. But did not reach the key hint for explaining it by pigeonhole principle. I thought the angle approach could work but didn't find the way to go.
I assume the circles are equal. There are six rays $PO_i$, where $P$ is the common points. Two of them will make an angle smaller than $\frac{2\pi}{6}$, so the distance between the centers will be at most the radius.