Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined
by these three points.

The first point can be assigned coordinates without loss of generality. Call the central angles from
the first point to the second and third and . The range of can be restricted to because of symmetry, but can range from . Then

The probability that the interior of the triangle determined by the three points picked at random on the circumference of a circle
contains the origin is 1/4.