The central angle of the arc would be formed by drawing radii from the endpoints of the arc (X and Z) to the center of the circle (let's call it O). The arc will be proportional to the circumference of the circle as the central angle is proportional to 360. To put that another way:

(arc/circumference) = (central angle/360)

So if we have the measure of the central angle and the length of the arc, we know the circumference.

Well Statement 1 gives us the arc. Great.

Statement 2 tells us that inscribed angle r = 60, since it is equal to the other two angles in the triangle shown.

The inscribed angle r will be half of the measure of the central angle of the arc. That means that the central angle of the arc = 120, and that's what we need to know.

Thank you for your explanation.

so, circumference would be..

6/x=120/360
x=18 ...?

Well, the arc length that they give us is for major arc XYZ, if I'm reading the problem correctly. Since the angle for minor arc XZ would be 120, then the remaining angle for major arc XYZ would be 240. So 240/360 = 18/Circumference, so the circumference would be 27.

Thank you for patiently explaining all this. I understnd finally