According to Chuck Adams and from my experience with my first deer, a shot into the hindquarter with an arrow will kill a deer graveyard dead. In fact, they will bleed out alot faster than you would think.
I'm not advocating taking this shot, like Adams seems to do in his book, but if an accident occurs, it will turn out alright. your case is further proof.
Congrats....

The first one is the hardest.