MathDB

Let

A

be a closed and bounded set in the plane, and let

C

denote the set of points at a unit distance from

A

. Let

p \in C

, and assume that the intersection of

A

with the unit circle

K

centered at

p

can be covered by an arc shorter that a semicircle of

K

. Prove that the intersection of

C

with a suitable neighborhood of

p

is a simple arc which

p

is not an endpoint. M. Bognar

Problem Statement