Random chords

Chords longer than a side are gold. Switch how they are picked: two random points on the circle make about one chord in three longer; a random radius with a random point on it, about half; a random point in the disc taken as the midpoint, about a quarter. All three count as random, yet the answers differ, and so do the textures the chords weave. These three are picked for this particular circle, so drag it elsewhere or shrink it and the chords move with it. Straws are different: they are lines thrown on the table with no regard for the circle, and only the stretch that crosses it counts. Move the circle, shrink it, and still about half of what it catches is gold, as with the second way.