# A line segment of length 2 moves in the xy-plane such that it always touches both the coordinate axes?

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A line segment of length 2 moves in the xy-plane such that it always touches both the coordinate axes (see the image below). Find the area of the region swept out by the line segment.

posted Mar 1, 2017

16-4*pi
Since we have tangents at the points where the curves meet the axes, curves can only be quarters of the circle radius 2. This is further supported by x^2+y^2=4 which is true for any position of the line. One quarter of the shaded area= area of square side 2 minus one quarter of the area of the circle radius 2 i.e. (4-pi). Hence the total shades area =16-4*pi

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