To invert the circle S with center
first
find the points p and q on S lying on the line determined by
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The unit vector from
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So to find the point q, start at the center
That is, start at
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To find the point p, start at
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Using the formula for the inverse of a point, we see that inverting p and q in C gives
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and
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Then, the center of the inverted circle is the midpoint of p' and q'. That is, the center is
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The diameter of the inverted circle is the distance between p' and q', so the radius is
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Note the center of the inverted circle is NOT the inverse of the center of S. Click the picture for an animation.
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Return to definition of inversion