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In geometry, a 'circumscribed' planar shape or solid is one that encloses and "fits snugly" around another geometric shape or solid. Specifically, there must be no object similar to the circumscribed object but smaller and also enclosing the inner figure.
Familiar examples include circles circumscribed around polygons, and triangles or regular polygons circumscribed around circles. See in particular circumscribed circle.
More precisely, in the phrase "a circumscribed ''F'' of ''X''", the inner figure ''X'' is supposed to be a given, specific figure (such as, for example, "the circle centered at ''A'' with radius ''r''"), whereas ''F'' stands for a class of figures (such as, for example, "triangle"). Of these figures, a circumscribed one is a figure of minimal size among those of the same shape enclosing ''X''. Usually it is unique in size, but not necessarily in position and orientation.
The definition given above assumes that the objects concerned are embedded in two- or three-dimensional Euclidean space, but can easily be generalized to higher dimensions and other metric spaces.

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