CEMC Euclid, 2007

Combinatorics Difficulty 2.0 Junior Prove it Canada

In the diagram, the area of $\triangle ABC$ is 1. Trapezoid $DEFG$ is constructed so that $G$ is to the left of $F$ , $DE$ is parallel to $BC$ , $EF$ is parallel to $AB$ and $DG$ is parallel to $AC$ . Determine the maximum possible area of trapezoid $DEFG$ .

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.