In a square with integer side lengths, is it possible to find a point that's a rational number length away from all 4 corners?

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I believe that it's not possible.

Give an example, because this is an unproven problem in number theory. :)

|dw:1438879607827:dw|
\[h=\frac{1}{\sqrt{2}}a \cancel{ \in} \mathbb{Q}\]

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