9. A circle of radius 1 cm rolls around the inside of a regular
hexagon with all sides of length 4 cm, so that the circle is always
touching at least one of the hexagon walls. (See the diagram.)
The distance measured in centimetres that the centre of the
circle travels before the circle returns to where it began is:
√ 3
(A) 12 √
3 (B) 18 (C) 42 − 12
(D) 21 (E) 24 − 4
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