This is a STILL image.

It is NOT a movie.

Method B1

The static diagram, above, shows points F and G when they are on CA- and BA-produced.

In the circle through F, G, B and C, we see two chords, FC and GB, intersecting at a point A.
There is a classic theorem [Euclid's Elements, Book 3, Proposition 35] about intersecting chords that states that AF.AC = AG.AB.

We can prove this using the similar triangles AFG and ABC, and the fact that corresponding sides of similar figures are in the same ratio.

We can also see that in the circle through D, E, B and C, there are two chords CD and BE such that CD-produced and BE-produced meet at a point A. The same theorem applies, with D corresponding to F and E corresponding to G, namely that AD.AC = AE.AB. Again, we can use similar triangles, in this case ADE and ABC, to prove this ...

In the movie on the next page we look at the relation AD.AC = AE.AB by interpreting the products AD.AC and AE.AB as areas of rectangles.