Question

Identify a semicircle that contains c

Answer 1

A semicircle is exactly half of a circle. The only semicircle in the picture, using the labeled points, is one which starts on A and ends on B (or starts on B and ends on A). A and B are on exactly opposite sides of the circle, but there is no point exactly opposite C. 

This means that you can rule out answers which start or end with C. This eliminates answers: (a) semicircle ABC, (b) semicircle AC, and (c) semicircle CB... which are all of the other three answers. 

Assuming that the measure of arc BC is about 45 degrees, the answers arc measures would be: 

(a) ABC = 180+45 = 225 degrees 
(b) AC = 180-45 = 135 degrees 
(c) CB = 45 degrees 
(d) ACB = 180 degrees 

(d) is the only answer which measures 180 degrees, so it's the only one which is a semicircle. 

You specify arc ACB (instead of just AB) to mean "from A, through C, on to B." Arc measures are usually the shortest distance unless an intermediate point is specified that identifies the path. So, for example, arc BC is 45 degrees, but arc BAC is the long way around and is 360-45 = 315 degrees. 

In the case of a 180-degree arc, you can't really tell which is the shortest way around, so you could choose either path. Specifying ACB requires going through C on the top half of the circle.