# A Guide to the GRE/Circles

# Circles[edit]

### Rules[edit]

The area of a circle is π multiplied by the radius squared. The circumference of a circle is π multiplied by the diameter (twice the radius).

A circle is a set of points of equal distance from a given point. The number π has been developed by mathematicians to express the ratio of the circumference of a circle to its diameter. π ≈ 3.14.

An arc within a circle is equal to the fraction of the circumference that the arc's angle is a fraction of 360º, or the entire circle.

In the circle to the left, arc AB has a length of one fourth of the circumference of the circle

### Practice[edit]

1. A circle has an area of 1. What is its radius?

2. Square GHIJ is inscribed within the circle. If the square has an area of 64, what is the area of the circle?

3.

D is the center of the circle, and points E and F are both on the circle. If EF and DF are both equal to 5, what is the length of arc EF?

### Comments[edit]

### Answers to Practice Questions[edit]

1.

The area of a circle is multiplied by the radius squared.

= 1 Take the initial equation.

= Divide both sides by

= = = Take the square root of both sides.

2.

If the area of the square is 64, then the sides of the square are 8. If the sides of the square equal 8, the diagonal - and thus the diameter of the circle equals

3.

The triangle is an equilateral triangle, meaning its angles are 60º. This means the arc has a length of one sixth of the circumference of the circle, or which works out to