The equilateral triangle ABC has sides of length 1 unit and AB lies on the line XY. The triangle is rotated clockwise around B until BC lies on the line XY. It is then rotated similarly around C and then about A as shown in the diagram.
What is the length of the path traced out by point C during this sequence of rotations?
If you liked this problem, here is an NRICH task
that challenges you to use similar mathematical ideas.