Questions about what happened in The Da Vinci Code?

Sir Leigh Teabing turned in the Monk, when the police tried to arrest him he started shooting at them and accidentally shot Bishop Aringarosa. The Bishop asked about the Monk by name, Silas. At that point Fache knew the Bishop was behind the murders and The Bishop ratted out Teabing. Fache had been told by Bishop Aringarosa that he had information linking Langdon to the murder in the museum.