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2004 AMC 10AProblem 22P21-25~5 minPrint
CirclesTriangles: Area & PythagoreanAdd construction lines/points (drop altitudes, extend segments, connect centers)Set up the equation/formula and compute; no special trick needed

Square ABCDABCD has side length 22 . A semicircle with diameter AB‾\overline{AB} is constructed inside the square, and the tangent to the semicircle from CC intersects side AD‾\overline{AD} at EE . What is the length of CE‾\overline{CE} ?

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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. Also appeared as 2004 12A #18.