Walking along a radial line is shorter than walking along the circumference on which the chords originates. This error is more pronounce where the curve has a high gradient. This happens at the end of the radius near the circumference where the shorter cords are.
The situation is the same as the radius rotates, undercounting at each turn does not make up for anything. As the radius makes a full turn, undercounting all along the way, the final result is still less. Undercounting these short cords results in a higher probability for long chords.
Ok?
