Editing Circle (section)

==Inscription in or circumscription about other figures==
In every [[triangle]] a unique circle, called the [[Incircle and excircles of a triangle|incircle]], can be inscribed such that it is tangent to each of the three sides of the triangle.<ref>[http://mathworld.wolfram.com/Incircle.html Incircle – from Wolfram MathWorld] {{webarchive|url=https://web.archive.org/web/20120121111333/http://mathworld.wolfram.com/Incircle.html |date=2012-01-21 }}. Mathworld.wolfram.com (2012-04-26). Retrieved on 2012-05-03.</ref>

About every triangle a unique circle, called the circumcircle, can be circumscribed such that it goes through each of the triangle's three [[Vertex (geometry)|vertices]].<ref>[http://mathworld.wolfram.com/Circumcircle.html Circumcircle – from Wolfram MathWorld] {{webarchive|url=https://web.archive.org/web/20120120120814/http://mathworld.wolfram.com/Circumcircle.html |date=2012-01-20 }}. Mathworld.wolfram.com (2012-04-26). Retrieved on 2012-05-03.</ref>

A [[tangential polygon]], such as a [[tangential quadrilateral]], is any [[convex polygon]] within which a [[inscribed circle|circle can be inscribed]] that is tangent to each side of the polygon.<ref>[http://mathworld.wolfram.com/TangentialPolygon.html Tangential Polygon – from Wolfram MathWorld] {{webarchive|url=https://web.archive.org/web/20130903051014/http://mathworld.wolfram.com/TangentialPolygon.html |date=2013-09-03 }}. Mathworld.wolfram.com (2012-04-26). Retrieved on 2012-05-03.</ref> Every [[regular polygon]] and every triangle is a tangential polygon.

A [[cyclic polygon]] is any convex polygon about which a [[circumcircle|circle can be circumscribed]], passing through each vertex. A well-studied example is the cyclic quadrilateral. Every regular polygon and every triangle is a cyclic polygon. A polygon that is both cyclic and tangential is called a [[bicentric polygon]].

A [[hypocycloid]] is a curve that is inscribed in a given circle by tracing a fixed point on a smaller circle that rolls within and tangent to the given circle.