On a sheet of paper draw a circle and name its center "F_1". Then pick a point and call it F_2.
Fold the paper so that F_2 meet the circumference at least 50 times (25 points and their opposite through the diameter):
What do you get if the distance between F_1 and F_2 is less than the circle radius?
What do you get if the distance between F_1 and F_2 is greater than the circle radius?
What do you get if the distance between F_1 and F_2 is equal than the circle radius?
By the way, did you notice the relation between the circle radius and the addition or the difference between the highlighted distances?
