Pseudohyperbolic disk

The picture on the left shows the usual disk of radius r centered in the origin.
The picture on the right shows the pseudohyperbolic disk with center a and radius r.
It is obtained from the disk on the left applying the Möbius transformation φ_a.
The point a is marked with black color.

It is known that the pseudohyperbolic disk with center a and radius r
coincides with the Euclidean disk with center c and radius s, where
c = a (1 - r²) / (1 - r² a²)    and    s = r (1 - a²) / (1 - r² a²).

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