A semicircle has center M and diameter AB. MN is perpendicular to AB, with N on the semicircle. If |MN| = 2 cm, find (a) |AB|, (b) the angle subtended by arc ANB at the center, and (c) the difference

The figure shows a semicircle with diameter AB. M is the center of the circle. The line segment MN is perpendicular to AB, and N is a point on the semicircle. Therefore, MN is the radius ($r$) of the semicircle.
Given $|MN| = 2$ cm.
So, the radius $r = 2$ cm.

The length of AB is the diameter of the semicircle, which is twice the radius.

The length of AB is $\boxed{\text{4 cm}}$.

Arc ANB represents the entire semicircle. The angle subtended by a semicircle at its center is $180^\circ$.
The angle is $\boxed{180^\circ}$.

The length of the line segment $\overline{AB}$ is the diameter, which is 4 cm.
The length of arc ANB is the circumference of a semicircle, given by the formula $\pi r$.
Length of arc ANB $= \pi \times 2 \text{ cm} = 2\pi \text{ cm}$.
The difference in length is the absolute difference between the arc length and the diameter:

Using $\pi \approx 3.14159$:

To convert this to millimeters, multiply by 10 (since $1 \text{ cm} = 10 \text{ mm}$):

Rounding to the nearest millimeter:

The difference in length is $\boxed{\text{23 mm}}$.