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'Triangular Wheel' printed from http://nrich.maths.org/
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?
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This problem is taken from the UKMT Mathematical Challenges.