Using the concept of the convex hull of a set of lines, a dual random triangle is defined by selecting three lines from a parent triangle of lines. The angles of the constructed triangle define the shape; calculation of the shape distribution is described. For a sequence of nested triangles constructed in this way it is shown that there is convergence to collinearity and to the collinear shape distribution derived by Mannion for a sequence of vertex-generated triangles.
"The shape of a sequence of dual random triangles." Bernoulli 12 (1) 55 - 63, February 2006.