der Täter
perpetrator
A person who has committed a crime or another unlawful act.
Die Polizei konnte den Täter kurz nach dem Einbruch festnehmen.
The police were able to arrest the perpetrator shortly after the burglary.

perpetrator / culprit
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perpetrator
A person who has committed a crime or another unlawful act.
Die Polizei konnte den Täter kurz nach dem Einbruch festnehmen.
The police were able to arrest the perpetrator shortly after the burglary.

The word 'Täter' (perpetrator/culprit) derives directly from 'die Tat' (an action or a crime). The ending '-er' denotes a person who does something. A 'Täter' is therefore literally a person who commits an act.
Jede kriminelle Tat hat einen Täter.
Every criminal act has a perpetrator.
In legal and police contexts, 'Täter' (perpetrator) is often used with certain verbs. Typical combinations are 'den Täter fassen' (to catch the perpetrator), 'den Täter ermitteln' (to identify the perpetrator), or 'den Täter überführen' (to prove the perpetrator's guilt).
Die Polizei hofft, den Täter bald zu fassen.
The police hope to catch the perpetrator soon.
In the language of the police, the justice system, and the media, 'Täter' (perpetrator) is the neutral and factual standard term for a person who has committed a crime.
Der Täter wurde zu einer Haftstrafe verurteilt.
The perpetrator was sentenced to prison.
Outside of a criminal context, 'Täter' (culprit) is often used humorously or ironically for someone who has committed a small, undesirable action.
Der Täter, der den letzten Keks gegessen hat, soll sich bitte melden!
The culprit who ate the last cookie should please come forward!
victim / sacrifice
'das Opfer' and 'der Täter' often belong to the same situation, for example a crime or an accident involving blame. But they refer to opposite roles. 'das Opfer' is the person who suffers harm. 'der Täter' is the person who committed the act. Learners may confuse the words because both often appear together in police reports or the news. The important question is: Who did something bad? That is the 'Täter'. Who was harmed? That is the 'Opfer'.

Die Polizei sucht den Täter, der das Fahrrad gestohlen hat.
The police are looking for the perpetrator who stole the bicycle.
Das Opfer wurde nach dem Unfall sofort ins Krankenhaus gebracht.
The victim was taken to the hospital immediately after the accident.