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Let's say I have a square inscribed into circle. Then how do you call the circle in relation to the rectangle?

Now I need proper naming convention for shapes in general.

inscribed rectangle sketch

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    Stay with the "inscribed in" relation. It won't cause any confusion. For the case of a rectangle inscribed in a circle, as AugSB's commented, the circle is the circumscribed circle. For a square inscribed in a rectangle, you would need to indicate _how_ it is inscribed. – 2017-02-13
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    The circle is the [circumscribed circle](https://en.wikipedia.org/wiki/Circumscribed_circle). I do not know any particular name for general shapes. – 2017-02-13
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    Image a video with fixed aspect ratio that has to fit into screen with given size (pixels), so entire video will be visible (letterboxing with symetrical black bars) I have a funcion called `GetInscribedRectangle` that calculates the position of the scaled video preview inside the UI element: `Rect GetInscribedRect(Size originalSize, Size sizeToFit)`. How would you describe the the second parameter? – 2017-02-13
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    "enclosed disk" or "biggest area enclosed disk" or "smaller area enclosing disk", more generally "enclosed _something_", or "enclosing _something_", for example "enclosed rectangle", or "enclosing rectangle" are common composite keywords in **image processing**. – 2017-02-13
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    Thks. I have written it as an answer with some added information. – 2017-02-16

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"enclosed" or "enclosing". But in general associated to a function that has to be either minimized of maximized. E.g., "biggest area enclosed disk" or "smaller area enclosing disk", more generally "enclosed something", or "enclosing something", for example "enclosed rectangle", or "enclosing rectangle" are common composite keywords in image processing. A common adjective for this class of objects is "bounding object".

In Matlab, for example, you can consult (https://fr.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects)

A more general site is (http://www.mlahanas.de/CompGeom/opt_bbox.htm)