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?

(In reply to re(2): According to Geometer's Sketchpad... (spoiler) by Charlie)

Oh, I'm sorry.  The triangle DEF is not what I meant by "enclosed triangle".  The enclosed triangle to which I was refering is entirely interior to ABC.  Its vertices are: the intersection of AE and BF, the intersection of BF and CD, and the intersection of CD and AE.

Posted by McWorter on 2005-08-23 20:28:19