The problem of the week is a regular instalment here at the geometry forum. Each weekend a high-school level geometry problem will be posted (though levels may be different in the summer), and the following weekend a summary of solutions will be posted.
Please do not post solutions to the problem of the week; instead mail you answer along with as detailed a description of your method as necessary/possible to firstname.lastname@example.org. Solutions should be received by midnight Friday so they can be combined and posted over the weekend.
Problem of the Week 7/26- 7/30 1993
This problem I originally saw on geometry.puzzles a few months ago. It took me a long time to solve, and I really enjoyed it.
Construct a triangle ABC. Find points D on AC and E on BC such that, if you were to draw the segment DE, it would be parallel to AB. (But don't draw DE.) Now draw segments BD and AE, and label their intersection F. If the area of the quadrilateral CDFE = 4 *and* the area of the triangle ABF = 4, what is the area of triangle ABC?
PS Apologies for being 2 days late with this post. You may all have until Sunday to send your solutions. :)