Jason is a farmer who lives in Sussex Inlet. Jason has a perfectly circular field with a radius of 200m. A new bypass for the local village is built which cuts off part of his field with a straight fence.Which one of the following must be true?
选项：

A:The perimeter of the field is more than it was before it was cut.
B:The fence is more than 200m long.
C:The distance from the centre of the circle to the farthest point of the fence is 200m.
D:The distance from the centre of the circle to the closest point of the fence is more than 100m.