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2008 AMC 10AProblem 19P16-20~5 minPrint
Transformations & SymmetryCirclesTriangles: Area & PythagoreanSet up the equation/formula and compute; no special trick needed

Rectangle PQRSPQRS lies in a plane with PQ=RS=2PQ=RS=2 and QR=SP=6QR=SP=6 . The rectangle is rotated 90∘90^\circ clockwise about RR , then rotated 90∘90^\circ clockwise about the point SS moved to after the first rotation. What is the length of the path traveled by point PP ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.