Determine the mean length of a chord, which is randomly chosen in a circle with radius \(r\). Consider separately the following ways how to randomly choose a chord:

(1) For symmetry reasons, the direction of the chord can be fixed in advance. Draw the diameter of the circle, which is perpendicular to this direction. The midpoints of the chords are uniformly distributed over the whole length of the diameter.

(2) For symmetry reasons, one end point of the chord can be fixed at the periphery of the circle. The direction of a chord is uniformly distributed over the interval in \([0, \pi]\).

(3) How do you explain the different results obtained under (1) an (2)?