Does a divorce occur by saying: "You are divorced if you are hiding something else from me that I do not know about this problem," and then it becomes clear that she was hiding something? And what is the ruling on sexual intercourse that took place in this situation? And is expiation required if the divorce occurred or did not occur?

What the questioner did is an oath of divorce. And since his wife concealed what transpired between them, he is obliged to divorce her according to the majority of scholars. If this was the first or second divorce, he may reconcile with her before her waiting period (iddah) expires, and intercourse would constitute a valid reconciliation, and there is no sin upon him. However, if this was the third divorce, she has become irrevocably divorced from him and is unlawful for him. There is no sin upon him for the intercourse due to his ignorance of the unlawfulness, but the sin falls upon her. Some scholars hold that an oath of divorce necessitates an expiation for an oath when it is broken, and this is the view of Sheikh Al-Islam Ibn Taymiyyah. Therefore, he is only required to offer expiation, and there is no sin upon him for the intercourse. However, the view of the majority is more preponderant.