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This is question 5 on page 20 of the book Complex Analysis by Lars Ahlfors. I have no idea how to answer that problem:

Find the radius of the spherical image of the circle in the plane whose center is $a$ and radius is $R$.

Here spherical image means: the image of a subset of complex numbers under the identification of the complex plane with the sphere $\Bbb S^2$ (the Riemann sphere) by stereographic projection:

Riemann Sphere

Thanks.

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    You need to post more details about this problem. Very few people will have this book. In order to discuss an image, we need to know what the map is.2012-09-03
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    @DrKW the map is the stereographic projection,also one should know the metric induced by the Riemann sphere to understand the problem.regards.2012-09-03
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    I used to have Ahlfors’s book, but I forget whether the plane is placed so as to pass through the center of the sphere or so as to be tangent to the sphere at the lowest point. This does affect the answer, so I have to agree with @Kris.2013-04-18
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    @Lubin Thanks for point that out. The plane is placed as in the image.2013-04-18

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