Here's the question :

Suppose C is a circle and for each a,b belonging to C, define d(a,b) to be the distance along the line segment form a to b. Then d is a metric on C.

So a and b are points on the circle C and you measure the "distance from a to b" along the straight line from a to b.

Now i don't really understand the meaning of this statement :

The fact that the route from a to b goes outside C is irrelevant ; a metric is a simply a function defined on ordered pairs and does not take into account any "route traveled" from one point to another.

Are'nt we suppose to define the metric within the given set, which in this case would be the circle C ?