Step 1:
The Poincare distance between two points $A = (x_1, y_1)$ and $B = (x_2, y_2)$ in the Poincare disk is given by the formula:
$$d(A, B) = \operatorname{arcosh}\left(1 + \frac{2|A - B|^2}{(1 - |A|^2)(1 - |B|^2)}\right)$$
where $|A|$ is the Euclidean norm of
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