(a) 10 points dividing a circle into 10 equal arcs are connected in pairs by 5 chords.
Is it necessary that two of these chords are of equal length? (b) 20 points dividing a circle into 20 equal arcs are connected in pairs by 10 chords.
Prove that among these 10 chords there are two chords of equal length.(VV Proizvolov, Moscow) geometrycombinatorial geometrypointscirclesarcchord