GMAT -Circles Flashcards
Radius
The radius of a circle is the distance from the center to any point on the circumference of a circle.
Therefore, the radius of a circle is half the diameter.
Diameter
The diameter is the longest straight line that can be drawn in a circle. The diameter is the distance from
one edge of a circle to another, through the center.
Circumference
The circumference is the distance around the perimeter of the circle.
Chord
A chord is any line inside a circle joining two points on the edge of the circle. Formally, the diameter is the
longest chord in the circle (however, it is extremely rare for the GMAT to call the diameter a chord).
Sector
A sector is a “slice” of the circle. It is an area of the circle bordered by two radii and part of the
circumference.
Arc
A portion of the circumference of a circle.
Minor arc
A minor arc is an arc that is LESS THAN half of the circle.
Major arc
A major arc is an arc that is MORE THAN half of the circle.
Tangent
Any line tangent to a circle is perpendicular to the radius. It touches the circle at only one point.
Area
πr^2
Circumference
2πr
Arc length
(measure of central angle) / (360 degrees) = (length of arc) / (circumference of circle)
Sector area
(measure of central angle) / (360 degrees) = (area of sector) / (total area)
Solving Circle Questions
Since almost every circle formula involves (or can be expressed with) the radius, always find the radius in any
Circle Question.
Arcs and Sectors
Since both arcs and sectors are related to the measure of the central angle, another way to express the relationship between arcs, sectors, and the rest of the circle is as follows:
(measure of central angle) / (360 degrees) = (area of sector) / (total area) = (length of arc) / (circumference of circle)
