20 MARK QUESTION, Let E; F be 2 points in the plane, EF has length 1, and let N be a, Mathematics

20 MARK QUESTION, Mathematics

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Let E; F be 2 points in the plane, EF has length 1, and let N be a continuous curve from E to F.
A chord of N is a straight line joining 2 points on N.
Prove if 0 < E; F < 1, and N has no chords of length E or F parallel to EF, then N has no chord of length E + F parallel to EF.
Prove that N has chords of length 1/X parallel to EF for all positive integers X

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20 MARK QUESTION, Mathematics

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