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Some properties of a regular 11-gon

A regular 11-gon is defined by points A, B, C, ..., J, K. Diagonals CE, CF, CG, CH, DF, DK and HK are drawn. Then intersection points L, M, N and O are defined as shown in the figure. Prove the following statements:
  • b=c,
  • d=e,
  • triangles CLM and CON are congruent,
  • a=l (that is, AB=DL).