Useful Definitions
arc: a curved line that is part of the circumference of a circle chord: a line segment within a circle that touches 2 points on the circle. circumference: the distance around the circle. diameter: the longest distance from one end of a circle to the other. origin: the...
Learn More
Introduction to circles
Definition: A circle is the locus of all points equidistant from a central point. A circle is a type of line. Imagine a straight line segment that is bent around until its ends join. Then arrange that loop until it is exactly circular – that is, all points along that line...
Learn More
Chords & Radii
All the “parts” of a circle, such as the radius, the diameter, etc., have a relationship with the circle or another “part” that can always be expressed as a theorem. The two theorems that deal with chords and radii (plural of radius) are outlined...
Learn More"A circle is the reflection of eternity."
It's got no beginning and it's got no end - and if you put a few circles over one another, you'll get a spiral.
About Us
Circles.org is a mathematics resource to those who are learning about the math of circles.
On this website you will find explanations about the math of circles, circle formulas and equations, and some useful examples & exercises.
Our mission is to make sure your understanding of the geometry of circles would improve upon visiting our website.
Please feel free to contact us using our contact us page. We look forward to hearing from you.
To add a bit of a funner part to our site, we’ve included lyrics to various ‘circles’ songs. We hope you like them!
Circles.org
Properties of Circles
- Center – A point inside the circle. All points on the circle are equidistant (same distance) from the center point.
- Radius - The radius is the distance from the center to any point on the circle. It is half the diameter.
- Diameter - The distance across the circle. The length of any chord passing through the center. It is twice the radius.
- Circumference - The circumference is the distance around the circle.
- Area - Strictly speaking a circle is a line, and so has no area. What is usually meant is the area of the region enclosed by the circle.
- Chord - A line segment linking any two points on a circle.
- Tangent - A line passing a circle and touching it at just one point.
- Secant - A line that intersects a circle at two points.
Circumference of a Circle
If you measure the distance around a circle and divide it by the distance across the circle through the center, you will always come close to a particular value, depending upon the accuracy of your measurement. This value is approximately 3.141592… We use the Greek letter PI (pronounced Pi) to represent this value. The number PI goes on forever. However, using computers, PI has been calculated to over 1 trillion digits past the decimal point.
The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. PI is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to PI. This relationship is expressed in the following formula: C / D = PI
where C is circumference and D is diameter. You can test this formula at home with a round dinner plate. If you measure the circumference and the diameter of the plate and then divide C by D, your quotient should come close to PI. Another way to write this formula is: C= PI x D where x means multiply. This second formula is commonly used in problems where the diameter is given and the circumference is not known.