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Trying to wrap my head around inversions. I understand it takes things from inside to outside, such that

$\text{distance from some point inside circle} + \text{ distance to new point}=r^2$

Where $r$ is radius of circle of inversion.

How would this look with a figure not just one line? For example a triangle inscribed in a circle? I know angles are supposed to be preserved.

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    Let $O$ be the centre of the circle, $P$ our point "inside" and $Q$ the point it s mapped to. Then $(OP)(OQ)=r^2$. (Your expression in terms of sums is not quite right.)2012-11-16
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    You might find this video enlightening: http://www.ima.umn.edu/~arnold/moebius/2012-11-16
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    http://i.stack.imgur.com/gQbt4.png2012-11-16

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