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**.