incenter
Very lowTechnical/Mathematical
Definition
Meaning
The center of the inscribed circle of a triangle (the circle tangent to all three sides).
In geometry, the point where the three angle bisectors of a triangle intersect; more generally, the center of the largest possible circle that can be inscribed within a given polygon.
Linguistics
Semantic Notes
Used exclusively in geometry and related mathematical fields. Not to be confused with 'incentre' (alternative spelling) or 'center' in general contexts.
Dialectal Variation
British vs American Usage
Differences
British English typically spells it 'incentre', while American English uses 'incenter'. The meaning and usage are identical.
Connotations
None beyond the technical mathematical meaning.
Frequency
Equally rare in both varieties, appearing only in mathematical texts.
Vocabulary
Collocations
Grammar
Valency Patterns
The incenter of [triangle]Find the incenterConstruct the incenterVocabulary
Synonyms
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Not used.
Academic
Used in geometry textbooks, papers, and lectures.
Everyday
Not used.
Technical
Used in mathematical proofs, geometric constructions, and computational geometry.
Examples
By Part of Speech
adjective
British English
- The incentre point is crucial for the proof.
American English
- The incenter coordinates were calculated.
Examples
By CEFR Level
- The incenter is inside the triangle.
- To find the incenter, you must construct the angle bisectors.
- The incenter's property of being equidistant from the sides makes it vital for certain optimisation problems in computational geometry.
Learning
Memory Aids
Mnemonic
INside the triangle, at the CENTER of the circle that fits snugly within it.
Conceptual Metaphor
The heart of the triangle (as the inscribed circle touches all sides equally).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not confuse with 'центр' (center) in a general sense. The specific Russian term is 'инцентр' or 'центр вписанной окружности'.
Common Mistakes
- Misspelling as 'insenter' or 'incencer'. Using it to refer to the center of a circumscribed circle (circumcenter).
Practice
Quiz
What is the incenter of a triangle?
FAQ
Frequently Asked Questions
No, it is a very low-frequency technical term used almost exclusively in geometry.
The incenter is the intersection of angle bisectors and the center of the inscribed circle. The centroid is the intersection of medians and the triangle's center of mass.
Generally, the term is specific to triangles. For other polygons, if a circle tangent to all sides exists, its center might be called an 'incenter', but this is only possible for tangential polygons.
In American English: /ˈɪnˌsɛntər/ (IN-sen-ter). In British English: /ˈɪnsɛntə/ (IN-sen-tuh).