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2009 Calculus #7: Strange Lines

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June 23, 2012
calculusgeometry

Problem Statement

A line in the plane is called strange if it passes through (a,0)(a,0) and (0,10āˆ’a)(0,10-a) for some aa in the interval [0,10][0,10]. A point in the plane is called charming if it lies in the first quadrant and also lies below some strange line. What is the area of the set of all charming points?
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