Identify the given information (center, diameter, circumference, area, chord/arc, or distance from center to a point).
If the diameter is given: use (r = frac{d}{2}).
If the circumference is given: use (r = frac{C}{2pi}).
If the area is given: use (r = sqrt{frac{A}{pi}}).
If the center and a point on the circle are given: use (r = sqrt{(x-x_0)^2 + (y-y_0)^2}).
If two points on the circle are given and the segment between them is a diameter: use (r = frac{d}{2}), where (d) is the distance between the points.
If the center and two points on the circle are given: compute the distance from the center to either point and set it equal to (r).
If a right triangle is formed with the center and a point on the circle (legs are given): use the Pythagorean theorem to find the distance from the center to the point.
If a chord length (c) and the distance (d) from the center to the chord are given: use (r = sqrt{d^2 + left(frac{c}{2}right)^2}).
If an arc length (s) and central angle (theta) (in radians) are given: use (r = frac{s}{theta}).
If a sector area (A) and central angle (theta) (in radians) are given: use (r = sqrt{frac{A}{frac{1}{2}theta}}).