A geometry problem by Worranat Pakornrat

Geometry Level 4

Consider all sets of 4 points A,B,C,DA, B, C, D which satisfy the following conditions:

  • ABAB is an integer.
  • BC=AB+1BC = AB + 1 .
  • CD=BC+1CD = BC + 1.
  • DA=CD+1 DA = CD + 1.
  • AC=DA+1AC= DA + 1
  • AC AC divides AB×CD+BC×DA AB \times CD + BC \times DA .

Over all such sets, what is maxBD? \max \lceil BD \rceil ?

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