Question 6
The walls of a room are in the shape of a triangle $ABC$ with $\angle ABC = 90^{\circ}$, $\angle BAC = 60^{\circ}$, and $AB = 6$. Chong stands at the midpoint of $BC$ and rolls a ball toward $AB$. Suppose that the ball bounces off $AB$, then $AC$, then returns exactly to Chong. Find the length of the path of the ball.
Supplemental illustration (AI-generated):
Supplemental illustration (AI-generated):