Draw two intersecting circles of different sizes. (The problem can be
worked if they are the same size, but it is trivial.) Let the larger one
have a radius K times that of the smaller one. Label the three areas in the
"Venn Diagram" A, B, and C - where A is the area of the larger circle
outside the intersection, B is the intersection, and C is the area of the
smaller cirlce outside the intersection.
If A is to B as B is to C, find A/B as a function of K.
Or stated another way, if the ratio of the area of the larger circle outside
the intersection to the area of the intersection is equal to the ratio of
the area of the intersection to the area of the smaller circle outside the
intersection, what percent of the larger circle is outside the intersection?
Seems to me that I have seen a problem similar to this before, but I can't
remember exactly what it was. While trying to come up with whatever problem
I thought I had seen I cam up with this one. I had fun solving it. Now,
somebody tell me it's a trivial problem and the answer is clearly __________
. :-)
For those of you coming close the summer vacation, have a great one.
Bret Taylor Lake-Sumter Community College Leesburg, FL
"It matters not the subject taught, nor all the books on all the shelves.
What matters more, yes, most of all, is what the teachers are themselves."
John Wooden
John 3 : 3^3 + 3
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