deliberate / intent
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deliberate
An action or person characterized by careful thought and caution. One does not act impulsively, but thinks beforehand.
Er ist ein sehr bedachter Mensch, der keine vorschnellen Urteile fällt.
He is a very deliberate person who does not make hasty judgments.
'Bedacht' (deliberate/intent) is the past participle of the verb 'bedenken' (to consider something, to think about something). A 'bedachte' person or action is therefore one that has been well thought through.
Bitte bedenken Sie die Konsequenzen Ihrer Entscheidung.
Please consider the consequences of your decision.
The two meanings are easy to distinguish. If 'bedacht' stands alone or before a noun, it means 'careful/deliberate'. If the preposition 'auf' follows, it is the fixed expression meaning 'to place importance on something' or 'to be intent on something'.
Seine Antwort war ruhig und bedacht.
His answer was calm and deliberate.
In the meaning 'careful/deliberate', the adjective often describes people, actions, or statements. Typical combinations are 'ein bedachter Mensch' (a deliberate person), 'bedacht handeln' (to act deliberately), or 'eine bedachte Wortwahl' (careful choice of words).
Sie wählte ihre Worte sehr bedacht, um niemanden zu verletzen.
She chose her words very carefully so as not to hurt anyone.
This meaning exists only in the fixed construction 'auf etwas bedacht sein' (to be intent on something / to be careful to do something). The preposition 'auf' always requires the accusative here.
Als Politiker ist er stets auf seinen guten Ruf bedacht.
As a politician, he is always intent on protecting his good reputation.
careful / cautious
'vorsichtig' and 'bedacht' both describe behavior where you do not simply act quickly. 'vorsichtig' emphasizes more that you want to avoid danger, mistakes, or damage. 'bedacht' emphasizes more strongly that you think beforehand and decide calmly. 'bedacht' sounds a bit more considered and less directly related to a danger. You could say: someone who acts 'bedacht' thinks first; someone who acts 'vorsichtig' pays special attention.
Die Ärztin bleibt bedacht und erklärt erst alle Möglichkeiten.
The doctor remains composed and first explains all the options.
Beim Umzug stellt Tom die Gläser vorsichtig in den Karton.
During the move, Tom carefully puts the glasses into the box.