Your body burns a given number of calories per day at rest. This is known as your basal rate. Normally for seditary adult males, it is around 2500kcal/daily. Of course this number can vary to a great degree depending on many factors. This is why most doctors will put adult mail patients on a 2000kcal/day diet. This generally will give you a 500kcal/day caloric deficit. 7x500=3500kcal/week = 1lb weight loss per week.

Now, if you are only consuming 1200kcal/day, you ARE starving your body, and chances are your body will resist wight loss because it is in starvation mode. You need to consume your basal calories minus 500kcal/day to get a 1lb/week weight loss. If you are riding 100 miles per week, your body NEEDS more calories to fuel itself. That is why you are having such hunger pains. Keep an eye on your cal-out vs cal-in and keep your cal-in 500kcal lower than your cal-out. You have to include the calories burned on your rides in this calculation or you will not see consistent results and may cause medical problems.

Hope this helps.

EDIT: Just wanted to add... CONGRATS ON YOUR WEIGHT LOSS!!!!!