Paper 3, Section I, G

Consider a quadrilateral $A B C D$ in the hyperbolic plane whose sides are hyperbolic line segments. Suppose angles $A B C, B C D$ and $C D A$ are right-angles. Prove that $A D$ is longer than $B C$.

[You may use without proof the distance formula in the upper-half-plane model

$\left.\rho\left(z_{1}, z_{2}\right)=2 \tanh ^{-1}\left|\frac{z_{1}-z_{2}}{z_{1}-\bar{z}_{2}}\right| \cdot\right]$

*Typos? Please submit corrections to this page on GitHub.*