This is a companion to Problem 174 from Fall 2003.  I then asked a similar question for points on the rim of the disk.  Here I want you to look at the points on the surface of the disk.  Happy thoughts.

A disk of radius one is one unit from a wall of length two.  The disk is making one revolution per second about its center.  See the view from above on the left.  Once per second, one of the points on the surface of the disk flies off, proceeding along a straight line path; some of these liberated points will hit the wall, others will not.  What is the area of the set of points that will hit the wall?

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ã2004 Alberto L. Delgado