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Let $G \subsetneq \mathbb{R}^n$ be a domain and let $d_1$ and $d_2$ be twometrics on $G$. We compare the geometries defined by the two metrics to eachother for several pairs of metrics. The metrics we study include the distanceratio metric, the triangular ratio metric and the visual angle metric. Finallywe apply our results to study Lipschitz maps with respect to these metrics.

Inequalities and bilipschitz conditions for triangular ratio metric