You've been suspicious of Cersei and Jaime for quite some time now. However, you didn't expect your intuition to be correct. You were searching through the library at the red keep, when you stumbled upon a book. Upon reading through its pages, which detailed the traits of every child born to one of the seven houses, you discovered a disgusting fact

That book was undeniable proof that Cersei's three children can't be Robert's. She has been cheating on him, with her own brother, for a while now. You knew you had to confront her about this. So, you asked to meet her in private. When you revealed to her that you were aware of her shameful act, however, she didn't hesitate to confess everything with confidence

"Targaryens wed brothers and sisters for 300 years to keep bloodlines pure. Jaime and I are more than brother sister. Came into this world together, we belong together."