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Method A1

In this movie we move F to D and back again (and G to E and back again).
The movie suggests that FG is parallel to DE in all the positions shown.

You might now want to try to prove that FG is parallel to DE. Or you might want to show the movies on the next two pages first - these display more extreme positions for F.

We can prove that FG is parallel DE if we can prove that angle AGF = angle AED.
These angles are exterior angles of the cyclic quadrilaterals GBCF and EBCD.
How can we use this fact?

On the next page we show what happens as F moves beyond D to C and then all the way back to A.
We can use this movie to reinforce the conjecture that FG is parallel to DE, or to consider what happens to the circle through B, C and F as G approaches B.