It does not have to go out of the circle. When the kick-off is taken players of the opposing team must not enter the circle until the ball is in play (i.e. until it has been kicked and moves forwards).
What happens in most games is that the player taking the kick-off passes it to a player standing very close to him and that person then kicks it backwards. (The person taking the kick-off must kick it forwards and he cannot touch it again until another player has done so, so the kick-off cannot be made directly backwards).
Now, for your next question, what is the purpose of the small part circle drawn on the top edge of the penalty area?