  It has been known that the distribution of the random distances between two
uniformly distributed points within a convex polygon can be obtained based on
its chord length distribution (CLD). In this report, we first verify the
existing known CLD for arbitrary triangles, and then derive and verify the
distance distribution between two uniformly distributed points within an
arbitrary triangle by simulation. Furthermore, a decomposition and recursion
approach is applied to obtain the random point distance distribution between
two arbitrary triangles sharing a side. As a case study, the explicit
distribution functions are derived when two congruent isosceles triangles with
the acute angle equal to $\frac{\pi}{6}$ form a rhombus or a concave 4-gon.
