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2006 AMC 10AProblem 23P21-25~5 minPrint
CirclesSimilar & Congruent TrianglesTriangles: Area & PythagoreanAdd construction lines/points (drop altitudes, extend segments, connect centers)Set up the equation/formula and compute; no special trick needed

Circles with centers AA and BB have radius 3 and 8, respectively. A common internal tangent intersects the circles at CC and DD , respectively. Lines ABAB and CDCD intersect at EE , and AE=5AE=5 . What is CDCD ?

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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 2006 12A #16.