CEMC Fermat, 2005

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

A circle is drawn so that no part of it lies outside a regular hexagon. If such a circle does not touch all six sides of the hexagon, what is the maximum number of sides that it could touch?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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