theorem Th30:
  C in LSeg(A,B) & |.A-C.| = 1/2 * |.A-B.| implies |.B-C.| = 1/2 * |.A-B.|
  proof
    assume that
A1: C in LSeg(A,B) and
A2: |.A-C.| = 1/2 * |.A-B.|;
    |.A-B.| = |.A-C.| + |.C-B.| by A1,Th8;
    hence thesis by A2,EUCLID_6:43;
  end;
