In the first case, a value in (-1,1) is chosen, and a chord is drawn. Optionally, the chord can be rotated by a random angle. About half of the chords will have length greater than .

In the second case, a random point on the edge of the circle is chosen, and a chord is connected to the lowest point of the circle. Optionally, both points can be chosen randomly. About a third of the chords will have length greater than .

In the third case, a random point inside the circle is chosen, and this is used as the midpoint of a chord. About a quarter of the chords will have length greater than .