circumcircle
Definition
- Noun:
- A circle that passes through all vertices of a polygon: In geometry, the "circumcircle" is the unique circle that passes through each vertex of a given polygon, most commonly used for triangles or any cyclic polygon. The polygon is said to be inscribed in the circle, and the circle is circumscribed about the polygon.
Usage Examples
- Noun:
- Every triangle has a circumcircle that passes through its three vertices. (A geometric property of all triangles.)
- The circumcircle of a square is the circle that touches all four corners. (Describes the circle around a square.)
Advanced Usage
"Circumcircle of a triangle": In triangle geometry, the center of the circumcircle is called the circumcenter, which is the intersection point of the perpendicular bisectors of the sides.
- To find the circumcircle of a triangle, construct the perpendicular bisectors of two sides. (A method for determining the circle.)
"Circumcircle radius": The distance from the circumcenter to any vertex of the polygon.
- The radius of the circumcircle is often denoted as R in formulas. (Standard notation in geometry.)
Variants and Related Words
Circumcenter (n): the center of the circumcircle.
- The circumcenter is equidistant from all vertices of the polygon. (A defining property of the center.)
Circumscribed (adj): describing a shape that is drawn around another, such that the outer shape touches the inner at points.
- A circumscribed circle is another term for a circumcircle. (Synonymous usage.)
Synonyms
- Circumscribed circle: a more descriptive term for the same concept.
- Circumradius: though technically the radius, it is often used to refer to the circle itself in context.
Related Idioms
- No common idioms: "Circumcircle" is a technical term and does not appear in everyday idioms or phrasal verbs.