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**Method C2**

Here we again look at the locus of P for the relationship AP = *r* x BP.

We start with *r* = 1.2 again but this time increase it to 4 and then reduce it to 1/4 (ie 0.25).

Before running the movie it is worth asking what happens to the locus (ie the circle)

- as *r* becomes less than 1.2

- as *r* reaches 1

- as *r* becomes less than 1

- as *r* reaches 1/4

- when *r* = 4 and when *r* = 1/4 ?

On the next page we look at the triangle ABP and at the line segments from P to the positions of P where BP is a minimum and a maximum. We consider **why** P moves on a circle, ie we try to develop a **proof**.