Can there be drawn on a circle of radius a number of distinct points, so that the distance (measured on the chord) between any two points (from the considered points) is a rational number?
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Can there be drawn on a circle of radius $1$ a number of $1975$ distinct points, so that the distance (measured on the chord) between any two points (from the considered points) is a rational number?
Source: Međunarodna matematička olimpijada, shortlist 1975
Školjka 
a number of 
distinct points, so that the distance (measured on the chord) between any two points (from the considered points) is a rational number?