A defense of the Principle of Indifference

There is only one chord in this set (unless the random point happens to be the center)

There's only one chord that has a midpoint that falls on a radii of the circle. Or to put it another way, connect a line from the midpoint of the chord to the center of the circle, and then limit the set of chords to only ones that have a 90 degree angle to that line.

But if we pick any point in the circle, we can see that there are infinitely many chords with that point as their midpoint, so we have to narrow down the selection somehow. If we assume that distribution is random around the angle, we can pick a unique chord by using any one angle consistently. Or I believe we can pick an random angle each time and also get the same distribution?

/r/math Thread Parent