- #1

Mentallic

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[tex]x^2+y^2=1[/tex] (1)

[tex](x+1)^2+(y-1)^2=3-2\sqrt{2}[/tex] (2)

[tex](x-\frac{\sqrt{7}}{2})^2+(y-\frac{1}{2})^2=3-2\sqrt{2}[/tex] (3)

What I need is a circle (in general form like those above) that touches all 3 circles just once. This is possible just by looking at the graph of the 3 circles. I know that this 4th circle will have its centre somewhere along the line that is perpendicular and passing through the midpoint to the line passing through the centre of the circles (2) and (3). This equation comes to be:

[tex]3x+(2-\sqrt{7})y=0[/tex]

From here I'm stuck. Usually I would find the distance between the centres of 2 circles to find the radius of 1 circle if I know the other, but in this case the centre is variates depending on how large the radius is.