How did Caesar meet Cleopatra?

Cleopatra had been deposed by her brother soon after she ascended the throne. Caeser was at war with roman general Pompey who fled to Egypt after defeat by Caeser. When he arrived he was murdered by cleopatras brother. Caeser followed Pompey to Alexandria not knowing he had been killed. Cleopatra was camped with an army on the borders of Egypt prevented from entering by her brothers army. When she heard Caeser was in Alexandria she had herself smuggled through enemy lines in a bag used to transport carpets. She was delivered to Caeser as a carpet gift direct to her palace where Caeser was installed. There she was unveiled to him. They began a relationship and he confirmed her as queen. He fought the Alexandrian war against cleopatras brother and won. Cleopatra gave birth to a son caesarion, who cleopatra claimed was fathered by Caesar although Caesar never acknowledged him.
Caesar wanted to bring Cleopatra and her brother together to put a stop to the civil war in Egypt, as Rome was Egypt's protector. He also wanted to make arrangements for the repayment of the massive debt that Egypt owed him.