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Method B2

Here we show P as a point of intersection of two circles with centres at A and B.

If we let AB = 2 units, then when the circle centre B has radius 10 units, the circle centre A has radius 12 units and the circles just touch. When the circle centre B has a radius larger than 10 units, the circles no longer intersect or touch; eg when its radius is 11 units, the circle centre A has radius 1.2x11 = 13.1 units which means it competely encloses the other circle.

So far we have just considered the relationship AP = 1.2 x BP.
On the next page we vary the multiplier, ie we consider what happens to the locus of P for the relationship AP = r x BP, as r varies.