Good for you and wonderful for your daughter to have a parent who isn't afraid of the truth. I have hesitated too many times in the past to tell my D's the truth bc I was afraid of AH's anger at me for "spilling" the secret. Finally I learned that my D's anxiety and my own were so so so much lessened when I just told the truth to myself first and others second...
Sorry for the ramble... good for you for telling your D the truth... Kids know when something is not right and I think the anxiety of wondering what is up is so much worse than the truth...