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Method B1

Here we trace more of the locus of P - indeed, we trace the entire locus, which turns out to be a circle (although we haven't proved this yet).
Note: If we let AB = 2 units, then the extreme right of the circle is 10 units from B.

This astonishing way of defining a circle is attributed to Apollonius of Perga (circa 262 to 190 BCE).

Some students might claim that this result is 'obvious' - either through genuine insight, or because for them the circle is the most familiar and obvious curved shape. On the other hand, students with a wider geometric knowledge might be surprised that it is not an open shape, such as a parabola or hyperbola.

On the next page we illustrate how the locus can be constructed using intersecting circles - this also shows why the locus is 'bounded' - as the circles get bigger, they reach a size where they no longer intersect.