![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Inscribed_circles.svg/640px-Inscribed_circles.svg.png&w=640&q=50)
Inscribed figure
Geometric figure which is "snugly enclosed" by another figure / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Inscribed figure?
Summarize this article for a 10 year old
In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid.[1] To say that "figure F is inscribed in figure G" means precisely the same thing as "figure G is circumscribed about figure F". A circle or ellipse inscribed in a convex polygon (or a sphere or ellipsoid inscribed in a convex polyhedron) is tangent to every side or face of the outer figure (but see Inscribed sphere for semantic variants). A polygon inscribed in a circle, ellipse, or polygon (or a polyhedron inscribed in a sphere, ellipsoid, or polyhedron) has each vertex on the outer figure; if the outer figure is a polygon or polyhedron, there must be a vertex of the inscribed polygon or polyhedron on each side of the outer figure. An inscribed figure is not necessarily unique in orientation; this can easily be seen, for example, when the given outer figure is a circle, in which case a rotation of an inscribed figure gives another inscribed figure that is congruent to the original one.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Inscribed_circles.svg/275px-Inscribed_circles.svg.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Circumcentre.svg/220px-Circumcentre.svg.png)
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/e/ed/Rhombic_tricontahedron_cube_tetrahedron.png)
(Click here for rotating model)
Familiar examples of inscribed figures include circles inscribed in triangles or regular polygons, and triangles or regular polygons inscribed in circles. A circle inscribed in any polygon is called its incircle, in which case the polygon is said to be a tangential polygon. A polygon inscribed in a circle is said to be a cyclic polygon, and the circle is said to be its circumscribed circle or circumcircle.
The inradius or filling radius of a given outer figure is the radius of the inscribed circle or sphere, if it exists.
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.
For an alternative usage of the term "inscribed", see the inscribed square problem, in which a square is considered to be inscribed in another figure (even a non-convex one) if all four of its vertices are on that figure.