In geometry, an inscribe planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. Specifically, at all points where figures meet, their edges must lie tangent. There must be no object similar to the inscribed object but larger and also enclosed by the outer figure.
Familiar examples include circles inscribed in polygons, and triangles or regular polygons inscribed in circles.
More precisely, in the phrase "an inscribed F of X", the outer 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, an inscribed one is a figure of maximal size among those of the same shape enclosed by 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 threedimensional Euclidean space, but can easily be generalized to higher dimensions and other metric spaces.
The inradius or filling radius of a given perimeter is the radius of the inscribed circle of that perimeter.
