Circle problems are among the most common types of geometry questions that appear on the GMAT. As such, you must make sure that you are fully prepared for these problems on test day.
The first key to circle questions is understanding what a circle really is. A circle is defined as a collection of all of the points that are equidistant from a center point. This distance is defined as the radius of the circle and the diameter is defined as twice the radius. For this reason, the radius of a circle is the key measurement when working with circles. On circle problems, knowing or solving for the radius will almost always be essential.
After the radius, the most important number to understand is π. π is defined as the ratio between the circumference of a circle and its diameter. Thus, the formula for finding the circumference of a circle is 2πr. You should also know the formula for the area of a circle, which is πr2.
Once you understand the fundamentals and formulas of a circle, you must also be prepared to calculate sector areas and arc lengths. Sector area is the area of a slice of the circle, and arc length is the distance between two points along the circle. These are both calculated by setting up a ratio of the angle measure the arc or sector creates in the center of the circle to 360. This ratio is equal to both the sector area to the total area of the circle and the arc length to the total circumference of the circle.
Finally, when thinking in terms of Data Sufficiency and having ENOUGH information to solve a given problem, keep in mind that if you have any ONE of the following: Area, Circumference, Radius, or Diameter, you can solve for all of the others! By keeping these rules in mind you will be able to solve the vast majority of circle problems quickly, saving time for more advanced problems that appear later in the test. For examples in action and more tips on circles, see the Kaplan GMAT Video on Circles.
~Bret Ruber
