# 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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