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=2DB, BE=2EC, and CF=2FA. 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=3FA. 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)
If D is on the extended line AB and F on the extended line CA, rather than on their respective segments (E has to be the midpoint of segment BC; the numbers don't work out otherwise), the new triangle FED has an area 25/12 that of triangle ABC.
However, if for example, D is on segment AB but F is again on the extended line CA, not on segment CA, the new triangle, DEF, is 16/15 the area of ABC.

Posted by Charlie
on 20050823 20:19:18 