Ah... "This is that time they tell you about in high school when algebra will save your life."
Sorry, quote from a movie I saw once!
Circumference = diameter * 3.14
so a round pen that is 50 feet across will have a circumference of about 157 feet.
You want posts 8-10 feet apart, so divide 157 by either 8 or 10 and you have the number of posts you need (it won't come out even)
If you plan to use board fencing, most board fencing comes in 16' lengths, which means your posts need to be 8' apart.
If you haven't already, you'll want to get some stakes or flags and plant them where you want your posts before you start..... chalk or white spray paint is great for marking your circle.
Good luck - post a photo when you're done!