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Topic: Problem of the Week, 2
Replies: 0

 Problem of the Week Posts: 292 Registered: 12/3/04
Problem of the Week, 2
Posted: Jul 26, 1993 2:46 PM

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;
description of your method as necessary/possible
to pow@forum.swarthmore.edu. 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. :)