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Given a circle with radius between 2 and 6 units, students are given a set of 8 points and asked to identify whether they are on, inside or outside the circle locus.

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Consider the circle centre at the origin and of radius $\\var{r}$.

\n

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{graph}

\n

$A=(\\var{r},0))\\qquad B=(0,-\\var{r})\\qquad C=(\\var{r-1},\\sqrt{\\var{2*r-1}})\\qquad D=(-\\sqrt{\\var{2*r-1}},\\var{r-1})$
$E=(\\var{r-1},-\\var{r-1})\\qquad F=(-\\var{r-1},-2\\sqrt 2)\\qquad G=(1,\\var{r/2})\\qquad H=(\\var{r},-\\var{r})$

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radius of the circle

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Write down the equation of this circle.

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For the following points determine which lie on the circumference of this circle, which lie inside the circle and which lie outside the circle.

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