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Extreme Cases

The Circular Track problem gives an example of trying to find an answer by looking at an extreme case. Since the sizes of the two circles were not given, the conclusion is that the answer does not depend upon them, but only on the length of the indicated chord of the large circle that is tangent to the small circle. So we can look at the extreme case when the radius of the smaller circle is 0, in which case the chord of length 100 is a diameter of the larger circle, and the area of the track is simply the area of the larger circle, namely, tex2html_wrap_inline1111 . This does not prove that you get the same answer for different sizes of circles, but at least it gives you evidence of what the answer must be if it only depends upon the chord.

Carl Lee
Wed Apr 21 08:17:28 EDT 1999