circumcenter: meaning, definition, pronunciation and examples
Very LowTechnical/Academic
Quick answer
What does “circumcenter” mean?
The point in a triangle that is equidistant from all three vertices, formed by the intersection of the perpendicular bisectors of the triangle's sides.
Audio
Pronunciation
Definition
Meaning and Definition
The point in a triangle that is equidistant from all three vertices, formed by the intersection of the perpendicular bisectors of the triangle's sides.
In geometry, the center of the circumscribed circle (circumcircle) of any polygon, most commonly a triangle. In broader mathematical contexts, may refer to the corresponding point in certain other polygons or higher-dimensional figures.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or spelling. Both variants use the same spelling. The mathematical definition is identical.
Connotations
None beyond its precise mathematical definition.
Frequency
Equally rare and specialized in both dialects, used almost exclusively in geometry education and mathematical texts.
Grammar
How to Use “circumcenter” in a Sentence
[the] circumcenter of [a geometric figure]Vocabulary
Collocations
Examples
Examples of “circumcenter” in a Sentence
verb
British English
- This point can be circumcentred to define the circle.
- We need to circumcentre the triangle to proceed.
American English
- This point can be circumcentered to define the circle.
- We need to circumcenter the triangle to proceed.
adverb
British English
- The lines were drawn circumcentrally.
- The figure was constructed circumcentrally.
American English
- The lines were drawn circumcentrally.
- The figure was constructed circumcentrally.
adjective
British English
- The circumcentral point is crucial for this proof.
- We calculated the circumcentral distance.
American English
- The circumcentral point is crucial for this proof.
- We calculated the circumcentral distance.
Usage
Meaning in Context
Business
Never used.
Academic
Used in geometry textbooks, lectures, and mathematical papers.
Everyday
Virtually never used.
Technical
Used in mathematical discourse, computer-aided design (CAD), and engineering geometry.
Vocabulary
Synonyms of “circumcenter”
Neutral
Weak
Vocabulary
Antonyms of “circumcenter”
Watch out
Common Mistakes When Using “circumcenter”
- Confusing 'circumcenter' (from perpendicular bisectors) with 'incenter' (from angle bisectors).
- Misspelling as 'circumcentre' in American contexts (though this is acceptable in British English).
- Using it for shapes that cannot have a circumscribed circle (e.g., most quadrilaterals).
FAQ
Frequently Asked Questions
No. It is inside only for acute triangles. For a right triangle, it lies on the hypotenuse's midpoint. For an obtuse triangle, it lies outside the triangle.
Primarily to find the center and radius of the circle that passes through all vertices of a polygon (the circumcircle). This is useful in geometry, trigonometry, and CAD applications.
No. Only cyclic polygons (polygons whose vertices all lie on a single circle) have a circumcenter. All triangles are cyclic, but many quadrilaterals and higher-order polygons are not.
The circumcenter is the center of the circumscribed circle (from perpendicular bisectors). The centroid is the 'center of mass' or balance point (from medians). They are only the same point for an equilateral triangle.
The point in a triangle that is equidistant from all three vertices, formed by the intersection of the perpendicular bisectors of the triangle's sides.
Circumcenter is usually technical/academic in register.
Circumcenter: in British English it is pronounced /ˈsɜː.kəmˌsen.tər/, and in American English it is pronounced /ˈsɝː.kəmˌsen.tɚ/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think CIRCUM- (meaning 'around', like 'circumference') + CENTER. It's the center of the circle that goes AROUND the triangle.
Conceptual Metaphor
The impartial judge (equidistant from all three competing vertices).
Practice
Quiz
From which geometric constructions is the circumcenter of a triangle derived?