der Mittelpunkt
center
The point that lies at the center of something and attracts the most attention.
Bei der Familienfeier stand die Großmutter im Mittelpunkt.
At the family celebration, the grandmother was the center of attention.

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center
The point that lies at the center of something and attracts the most attention.
Bei der Familienfeier stand die Großmutter im Mittelpunkt.
At the family celebration, the grandmother was the center of attention.

This word is made up of 'Mittel' (middle) and 'Punkt' (point). So it literally describes the point in the middle of something.
Der geografische Mittelpunkt Deutschlands liegt in Thüringen.
The geographical center of Germany is in Thuringia.
The most common use is the fixed expression 'im Mittelpunkt stehen'. It means to receive the most attention.
Bei der Diskussion stand das neue Gesetz im Mittelpunkt.
The new law was at the center of the discussion.
Besides 'stehen' (to stand), 'Mittelpunkt' is often used with verbs that express active centering, such as 'etwas in den Mittelpunkt stellen' (to put something at the center) or 'in den Mittelpunkt rücken' (to move into the center/focus).
Der Redner stellte die Bedürfnisse der Bürger in den Mittelpunkt seiner Rede.
The speaker put the needs of the citizens at the center of his speech.
You can recognize the geometric meaning from words from mathematics or technology. Typical signal words are 'Kreis' (circle), 'Radius' (radius), 'Zirkel' (compass), or 'geometrisch' (geometric).
Der Radius ist der Abstand vom Mittelpunkt zum Rand eines Kreises.
The radius is the distance from the center point to the edge of a circle.
middle / center
'die Mitte' and 'der Mittelpunkt' can both mean the center of something. 'Die Mitte' is often an area: the middle of a room, a table, or a page. 'Der Mittelpunkt' is more precisely a specific point at the center. In addition, 'Mittelpunkt' can also mean that something or someone gets the most attention. Learners may confuse the words because both have to do with the center. As a simple guide: for a normal central area, 'Mitte' usually fits best; for an exact point or the focus of attention, 'Mittelpunkt' is more likely.

Beim Geburtstag stand das Kind den ganzen Abend im Mittelpunkt.
At the birthday party, the child was the center of attention all evening.
In der Mitte des Raumes steht ein großer Tisch.
There is a large table in the middle of the room.