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Omni-MATH / Given that A, B, and C are noncollinear points in the plane with integer coordinates such that the distances AB, AC, and BC are integers, what is the smallest possible value of AB?

Problem

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problem

Given that AA, BB, and CC are noncollinear points in the plane with integer coordinates such that the distances ABAB, ACAC, and BCBC are integers, what is the smallest possible value of ABAB?
Plain-text mathematical notation (without MathML)
Given that A, B, and C are noncollinear points in the plane with integer coordinates
such that the distances AB, AC, and BC are integers, what is the smallest possible value of AB?
Original LaTeX notation
Given that $A$, $B$, and $C$ are noncollinear points in the plane with integer coordinates
such that the distances $AB$, $AC$, and $BC$ are integers, what is the smallest possible value of $AB$?

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Source and history

task_id
5071cb95-7d90-51c9-8be8-f0032feaa0cd
task_key
test--5071cb95-7d90-51c9-8be8-f0032feaa0cd
task_revision_id
1
config / split
/ test

Official source

initial import