Question 58
A regular hexagon with side $1$ is given. Consider an equilateral triangle with side $1$ inside the hexagon, with two vertices constrained to the perimeter of the hexagon. We move the equilateral triangle so that one of the two constrained vertices goes exactly once around the perimeter of the hexagon. What is the length of the path travelled by the unconstrained vertex?
(A) $\pi / 2$
(B) $\frac{\pi \sqrt{3}}{3}$
(C) $8 \sqrt{3}-12$
(D) $(4 \sqrt{3}-6) \pi$
(E) None of the above.
(A) $\pi / 2$
(B) $\frac{\pi \sqrt{3}}{3}$
(C) $8 \sqrt{3}-12$
(D) $(4 \sqrt{3}-6) \pi$
(E) None of the above.