  The point pair function $p_G$ defined in a domain $G\subsetneq\mathbb{R}^n$
is shown to be a quasi-metric and its other properties are studied. For a
convex domain $G\subsetneq\mathbb{R}^n$, a new intrinsic quasi-metric called
the function $w_G$ is introduced. Several sharp results are established for
these two quasi-metrics, and their connection to the triangular ratio metric is
studied.
