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The equilateral triangle ABC has sides of length 1 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.

*This problem is taken from the UKMT Mathematical Challenges.*