vicinity / circumcircle
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vicinity
An area or region located within a certain distance around a central point.
Wir suchen eine neue Wohnung im Umkreis von zehn Kilometern um meine Arbeitsstelle.
We are looking for a new apartment within a ten-kilometer radius of my workplace.
circle
A person's social environment; the circle of people with whom someone has regular contact.
Er bespricht wichtige Entscheidungen nur im engsten Umkreis seiner Familie.
He discusses important decisions only within the closest circle of his family.
circumcircle
In geometry, a circle that passes through all vertices of a polygon.
Der Lehrer erklärte, wie man den Mittelpunkt des Umkreises eines Dreiecks konstruiert.
The teacher explained how to construct the center of the circumcircle of a triangle.
The word is made up of the preposition 'um' (around) and the noun 'der Kreis' (circle). So it literally describes a circle around something, which is the basic idea in all meanings.
Im weiten Umkreis gab es kein einziges Haus.
There was not a single house in the wider vicinity.
To describe a geographic area, the fixed expression 'im Umkreis von' (within a radius of) is almost always used, followed by a distance. The central point is introduced with 'um' (around).
Alle Filialen im Umkreis von 50 Kilometern um Hamburg werden heute beliefert.
All branches within a 50-kilometer radius of Hamburg will be supplied today.
When referring to the social environment, 'Umkreis' (circle) is often combined with adjectives like 'eng' (close), 'persönlich' (personal), or 'familiär' (family-related). It then describes the group of people who are close to someone.
Diese Information ist nur für den engsten Umkreis der Geschäftsführung bestimmt.
This information is intended only for the innermost circle of the management.
This meaning belongs to the technical language of geometry. You can recognize it from words like 'Dreieck' (triangle), 'Polygon' (polygon), 'Mittelpunkt' (center), or 'konstruieren' (to construct).
Jedes Dreieck besitzt genau einen Umkreis.
Every triangle has exactly one circumcircle.
surroundings / environment
Umgebung generally refers to the area around a place. Umkreis places more emphasis on a center and on a definable or measurable distance from that center. Use Umgebung for the surrounding area as a whole and Umkreis when the distance or radius is important.
Im Umkreis von fünf Kilometern gibt es mehrere Bahnhöfe.
There are several train stations within a radius of five kilometers.
Die Umgebung des Bahnhofs ist auch am Abend gut beleuchtet.
The area around the train station is well lit even in the evening.
