A CIRCLE OF RADIUS 1 CM ROLLS AROUND THE INSIDE OF A REGULARHEXAGON...

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