Consider two points $P$ and $Q$ inside the Poincare disk, at distances $r_1$ and $r_2$ respectively from the origin $O$. Furthermore, $P$ and $Q$ form an angle of $\theta$ at the origin. Is there any closed form result for the radius of the orthogonal circle that is used to construct the geodesic through $P$ and $Q$?
2026-03-29 13:27:44.1774790864
Radius of inversion circle in the Poincare Disk model
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