excircle
Very RareTechnical/Mathematical
Definition
Meaning
A circle that is tangent to one side of a triangle and to the extensions of the other two sides.
In geometry, a circle outside a given triangle that touches one side and the extensions of the two adjacent sides.
Linguistics
Semantic Notes
A specialized geometric term; only understood in mathematical contexts. Opposite of 'incircle' (inscribed circle). Part of triangle geometry terminology.
Dialectal Variation
British vs American Usage
Differences
No differences in meaning or usage; identical in both varieties. Both use the same spelling and pronunciation.
Connotations
Purely mathematical/technical, no cultural connotations.
Frequency
Extremely rare in both varieties, confined to geometry textbooks and advanced mathematics.
Vocabulary
Collocations
Grammar
Valency Patterns
The excircle [is tangent] to side AB.An excircle [touches] one side.The excircle [is constructed] outside the triangle.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Not used.
Academic
Used exclusively in geometry, trigonometry, and advanced mathematics.
Everyday
Never used.
Technical
Used in mathematical contexts, engineering geometry, CAD software.
Examples
By Part of Speech
adjective
British English
- The excircle centre is also called an excentre.
- Excircle properties are fascinating.
American English
- The excircle radius can be calculated.
- Excircle geometry involves tangents.
Examples
By CEFR Level
- This word is not used at A2 level.
- An excircle is a circle outside a triangle.
- The excircle touches one side.
- Each triangle has three excircles, each tangent to one side.
- The excircle's centre lies at the intersection of external angle bisectors.
- The radius of the excircle opposite vertex A is given by r_a = Δ/(s-a), where Δ is the area and s the semiperimeter.
- In advanced geometry, properties of the excircle are used to prove various triangle theorems.
Learning
Memory Aids
Mnemonic
EXcircle = EXternal circle; it's EXcluded from inside the triangle.
Conceptual Metaphor
None in common usage.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not confuse with 'вписанная окружность' (incircle). 'Excircle' is 'вневписанная окружность'.
- The prefix 'ex-' means 'outside', not 'former' here.
Common Mistakes
- Confusing 'excircle' with 'incircle'.
- Assuming it's a verb (to excircle).
Practice
Quiz
What is an excircle?
FAQ
Frequently Asked Questions
No, it's a very rare technical term used only in geometry.
Yes, every triangle has three excircles, each associated with one side.
An incircle is inside the triangle and touches all three sides; an excircle is outside and touches one side and the extensions of the other two.
Almost never; it's confined to geometry and related technical fields.