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,
. 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.