What does bicentric mean?
Bicentric is an adjective meaning having or relating to two centers. It is chiefly a technical term of geometry, where a bicentric polygon is one whose vertices all lie on a single circle (making it cyclic) and whose sides are all tangent to another circle (making it tangential). Every triangle is automatically bicentric, but for polygons with four or more sides the property is special enough to have inspired dedicated theorems, such as Fuss's theorem linking the radii of a bicentric quadrilateral's two circles. Beyond geometry, the word appears in scholarly contexts to describe systems, economies, or urban regions organized around two dominant centers rather than one. Formed from Latin bi- ('two') and Greek kentron ('center'), bicentric is precise and formal in register, essentially unknown in casual conversation, and valuable whenever a distinction between dual-centered and single-centered arrangements matters.
adjectiveHaving or relating to two centers. In geometry, describes a polygon that is both cyclic (all vertices on one circle) and tangential (all sides tangent to another circle); more generally, characterized by or organized around two centers.
- (geometry) Of a polygon: both cyclic and tangential, having an incircle and a circumcircle.
- Having, involving, or organized around two centers (used generally or in specialized fields such as linguistics or economics).
"The Fournier–Gagnier theorem characterizes bicentric quadrilaterals by a simple relation between their sides."
"Every triangle is bicentric, since it always possesses both an incircle and a circumcircle."
"The study treated London and Paris as a bicentric urban system linked by high-speed rail."
A square is the only regular polygon that is truly bicentric — its corners sit perfectly on one circle while its sides kiss another.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of bicentric
Bicentric combines the Latin prefix bi-, meaning 'two', with the root centric, ultimately derived from the Greek kentron, meaning a sharp point or pivot, which passed into Latin as centrum before entering English. The word belongs to the same family as central, concentric, and eccentric. It emerged in technical and mathematical usage, most notably in geometry, where mathematicians needed a compact term for polygons possessing both an incircle and a circumcircle.
How bicentric is actually used
Predominantly a technical term. Its most established use is in geometry, where 'bicentric' has a precise meaning for polygons; outside mathematics it appears mainly in academic writing describing systems, cities, or structures organized around two centers. Rare in everyday speech.
Easily confused with bicentric
Concentric means sharing a single common center, while bicentric means having or involving two distinct centers.
Eccentric means deviating from a center or being unconventional, whereas bicentric simply means having two centers.