circumcircle: meaning, definition, pronunciation and examples
C2Formal/Technical
Quick answer
What does “circumcircle” mean?
The circle that passes through all the vertices of a given polygon or triangle.
Audio
Pronunciation
Definition
Meaning and Definition
The circle that passes through all the vertices of a given polygon or triangle.
In geometry, the unique circle that encloses a polygon such that all its vertices lie on the circle's circumference. More broadly, it can refer to any encompassing boundary in metaphorical or technical contexts.
Dialectal Variation
British vs American Usage
Differences
No significant spelling or usage differences. Pronunciation differs slightly (see IPA).
Connotations
Purely technical term with identical meaning and application in both dialects.
Frequency
Equally rare and specialized in both UK and US English, limited to academic geometry, engineering, and computer graphics.
Grammar
How to Use “circumcircle” in a Sentence
The circumcircle of [a triangle/polygon]To construct/draw a circumcircle around [an object]Vocabulary
Collocations
Examples
Examples of “circumcircle” in a Sentence
verb
British English
- We need to circumcircle the polygon to find its centre.
- The software can automatically circumcircle any selected triangle.
American English
- The algorithm circumcircles the set of points.
- First, circumcircle the quadrilateral.
adverb
British English
- The points were arranged circumcircularly.
American English
- The vertices lie circumcircularly.
adjective
British English
- The circumcircle radius is a key parameter.
- We calculated the circumcircle properties.
American English
- The circumcircle center point is located here.
- Use the circumcircle equation.
Usage
Meaning in Context
Business
Not used.
Academic
Used in geometry, trigonometry, computer-aided design (CAD), and computational geometry papers.
Everyday
Virtually never used in everyday conversation.
Technical
Used in mathematics, engineering, architecture, and 3D modelling software documentation.
Vocabulary
Synonyms of “circumcircle”
Strong
Neutral
Weak
Vocabulary
Antonyms of “circumcircle”
Watch out
Common Mistakes When Using “circumcircle”
- Misspelling as 'circumcircle' (one 'c').
- Using it to refer to any circle drawn around an object, rather than one specifically passing through all vertices.
- Confusing it with 'circumference', which is the perimeter length.
FAQ
Frequently Asked Questions
No. Only cyclic polygons have a circumcircle. All triangles and regular polygons are cyclic, but an irregular quadrilateral may not be.
It is called the circumcenter.
An incircle is inscribed *inside* a polygon, touching all its sides. A circumcircle is circumscribed *outside*, passing through all its vertices.
Almost exclusively no. Its use is highly specialized to geometry, engineering, and related technical fields.
The circle that passes through all the vertices of a given polygon or triangle.
Circumcircle is usually formal/technical in register.
Circumcircle: in British English it is pronounced /ˈsɜː.kəmˌsɜː.kəl/, and in American English it is pronounced /ˈsɝː.kəmˌsɝː.kəl/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “None”
Learning
Memory Aids
Mnemonic
Think of 'circum-' (around, as in circumference) + 'circle'. It's the circle that goes *around* the shape, touching all its corners.
Conceptual Metaphor
A PERFECT BOUNDARY (The circumcircle represents an ideal, all-encompassing limit for a shape.)
Practice
Quiz
What is the primary defining feature of a circumcircle?