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: According to Geometer's Sketchpad... (spoiler) by Charlie)

You are so right!  I assumed D, E, and F were on the triangle, not outside it, without explicitly saying so.  Thanks for pointing this out.  I meant D is between A and B, E is between B and C, and F is between C and A.

Posted by McWorter on 2005-08-23 20:11:35