Let E; f be 2 points in the plane such that EF has length 1, and let L be a continuous curve from E to F. A chord of L is a straight line joining two points on L. Prove that if 0 < E; F < 1,and L has no chords of length a or b parallel to EF, then L has no chord of length e + f parallel to EF. Prove that K has chords of length 1/Xparallel to EF for all positive integers X. Must L have chords of length r parallel to EF for any real r with 0 < r < 1?