# Circle

### radius center called distance

In the language of **geometry**, a circle is the **locus** of points in a **plane** that are all at an equal **distance** from a single **point**, called the center of the circle. The fixed distance is called the radius of the circle. A line segment with each of its endpoints on the circle, that passes through the center of the circle, is called a diameter of the circle. The length of a diameter is twice the radius. The distance around a circle, called its circumference, is the length of the line segment that would result if the circle were broken at a point and straightened out. This length is given by 2πr, where r is the radius of the circle and π (the Greek letter π, pronounced "pie") is a constant equal to approximately 3.14159. Points lying outside the circle are those points whose distance from the center is greater than the radius of the circle, and points lying in the circle are those points whose distance from the center is less than the radius of the circle. The area covered by a circle, including all the points within it, is called the area of the circle. The area of a circle is also related to its radius by the formula A = πr ^{2}, where A is the area, r is the radius, and π is the same constant as that in the formula for the circumference. In the language of **algebra**, a circle corresponds to the set of ordered pairs (x,y) such that (x - a)^{2 }+ (y - b)^{2} = r^{2}, where the point corresponding to the ordered pair (a,b) is the center of the circle and the radius is equal to r.

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