Stroke size does not match after using Divide

[southwestform]

I want to take the first image, use Divide in Pathfinder, then delete the part of the circle that extends beyond the square. However, when doing this, the stroke from the square is not the same over the portion where the circle was. How can I get the stroke to match the size of the rest of the square? Thanks.

[Monika Gause]

Ungroup the result and move the circle away.

Or align the stroke to the inside.

Or apply a thicker stroke to the circle.