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Area Between Concentric Circles

Topic:
Area, Circle
A problem appeared in 1969 on a contest that asked about the area between concentric circles: http://artofproblemsolving.com/wiki/index.php?title=1969_AHSME_Problems/Problem_6. It seems there is not enough information at first, but try some things to see if you can get the area of the annulus from just the length of the chord that is given.