A geometry problem by Worranat Pakornrat

Geometry Level 4

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

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

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

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