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| Variation on a Classic (Posted on 2005-08-23) |
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In the classic problem you are given a triangle ABC with points D on AB, E on BC, and F on AC such that |AD|=2|DB|, |BE|=2|EC|, and |CF|=2|FA|. The lines AE, BF, and CD enclose a triangle inside triangle ABC. You are to find the area of this enclosed triangle relative to that of ABC. The answer is 1/7.
What if everything is the same except |BE|=|EC| and |CF|=3|FA|. What is the area of the enclosed triangle relative to that of ABC?
According to Geometer's Sketchpad... (spoiler)
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 | Comment 1 of 13
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the answer is 10.
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Posted by Charlie
on 2005-08-23 18:24:42 |
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