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Variation on a Classic (Posted on 2005-08-23) Difficulty: 3 of 5
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?

See The Solution Submitted by McWorter    
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re(2): According to Geometer's Sketchpad... (spoiler) | Comment 6 of 12 |
(In reply to re: According to Geometer's Sketchpad... (spoiler) by McWorter)

Yes, it should be 1/10, as I was taking the ratio the wrong way around.
  Posted by Charlie on 2005-08-23 20:22:30

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