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GMAT > Math > Geometry > Circle and Coordinate

GMAT Math Circle and Coordinate Overview

GMAT CAT Circle

Almost any GMAT problem regarding circles requires you to know about radius, diameter, and circumference. A circle, by technical definition, is a set of points in a plane that are at a fixed distance from a given point. That point is called the center.

Radius: The radius of a circle is the distance from the center of the circle to any point on the circle. Think of it as a ray going out from the center to the edge of the circle. The radius is usually indicated by the letter r.
Diameter: The diameter of a circle is the length of a line that goes from one side of the circle to the other and passes through the center. The diameter is twice the length of the radius, and it's the longest possible distance across the circle.
Circumference: The circumference of a circle is the distance around the circle. You can think of the circumference as the perimeter of the circle, although this isn't quite true. It's really more technically accurate to say you're trying to find the perimeter of a regular polygon with an infinite number of sides as it gets rounder and rounder. Rather than taking the time to figure out how many sides add up to infinity, just use this formula:
C = 2πr or C = πd

Arc: An arc of a circle is a portion along the edge of the circle. Because it runs along the circumference, an arc is actually a part of the circle.
Chord: A chord is a line segment cutting across a circle that connects two points on the edge of a circle. Those two points at the end of the chord are also the endpoints of an intercepted arc.
Tangent: A tangent line is one that intersects the circle at just one point. A good way to think of a tangent line in the real world is like a wheel rolling along a road. The road is tangent to the wheel.

GMAT CAT Coordinate Geometry

Coordinate geometry combines the study of algebra and planes with three-dimensional geometry. You can expect to encounter coordinate geometry questions on roughly ten percent of the problems on the GMAT. If you're not particularly savvy about coordinate geometry, it won't significantly affect your GMAT math score.

You may haven't encountered for GMAT coordinate geometry questions, so take just a minute to refresh your memory about a few relevant terms that may pop up on the GMAT.

Coordinate plane: The coordinate, or Cartesian, plane is a perfectly flat surface that contains a system in which points can be identified by their position using an ordered pair of numbers. This pair of numbers represents the points' distance from an origin on perpendicular axes. The coordinate of any particular point is the set of numbers that identifies the location of the point, such as (3, 4) or (x, y).
x-axis: The x-axis is the horizontal axis (number line) on a coordinate plane in which values or numbers start at the origin, which has a value of 0. Numbers increase in value to the right of the origin and decrease in value to the left. The x value of a point's coordinate is listed first.
y-axis: The y-axis is the vertical axis (number line) on a coordinate plane in which values or numbers start at the origin, which has a value of 0. Numbers increase in value going up from the origin and decrease in value going down. The y value of a point's coordinate is listed second.
Origin: The origin is the point (0, 0) on the coordinate plain. It's where the x- and y-axes intersect.
Ordered pair: Also known as a coordinate pair, this is the set of two numbers that shows the distance of a point from the origin. The horizontal (x) coordinate is always listed first, and the vertical coordinate (y) is listed second.
Ordinate: Ordinate is another way of referring to the y-coordinate in an ordered pair.
x-intercept: The value of x where a line, curve, or some other function crosses the x-axis. The value of y is 0 at the x-intercept. The x-intercept is often the solution or root of an equation.
y-intercept: The value of y where a line, curve, or some other function crosses the y-axis. The value of x is 0 at the y-intercept.
Slope: Slope measures how steep a line is and is commonly referred to as the rise over the run.

Although you won't be asked to define these terms, knowing what they mean is absolutely essential. Our instructors have prepared more detailed video explanations for GMAT CAT coordinate geometry. To see full lesson videos, buy our GMAT prep plans that best suits you.

GMAT Geometry Topics

Below are the topics covered under GMAT Geometry. Click on them to learn more: