Questions & Answers about Il est fatigué à tel point de délirer.
Can I use au point de instead of à tel point de in this sentence?
Why do we use the infinitive délirer instead of a full clause like qu'il délire?
Because the person who is tired is the same person who is delirious (il). When the subject is the same for both actions, we use the preposition de followed by an infinitive. If the subjects were different, you would use au point que followed by a conjugated verb.
Does délirer always mean a literal, medical delirium?
Is it ever correct to say à un tel point with the article un?
Yes, but not in this specific grammatical structure. When the phrase is followed by de plus an infinitive, you drop the article and just say à tel point. If you end the sentence there without adding the consequence, you will often hear à un tel point (to such a degree), for example: Il est fatigué, à un tel point !