- if the angle's vertex is in the center of the circle, then the degree of the angle and the arc are the same
- if the vertex is on the circle (an inscribed angle) then the angle measure is half the arc measure
- if the vertex is outside the circle, then the angle is half the difference of the two arcs
- if the vertex is inside the circle (but not smack in the middle) then the angle is half the sum of the two arcs
Remember that if two inscribed angles intercept (or capture) the same arc, then those angles are the same measure (and can be set equal to each other).
Also be familiar with the equation of a circle, particularly where the center and the radius show up.
For example:
A circle with center (2,-3) and a radius of 5 would look like
(x-2)^2 + (y+3)^2 = 25