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Properties of circles

In geometry, a circle is a shape made up of all the points on a plane at a fixed distance around a given point (the center). The equation for a circle is

{(x - h)}^{2} + {(y - k)}^{2} = r^{2}

, in which

h

and

k

represent the circle's center and

r

represents the circle's radius, the distance from the circle's center to any point on its perimeter. A circle with a center at

(4, 5)

and a radius of

10

, for example, could be expressed as

{(x - 4)}^{2} + {(y - 5)}^{2} = 100

Relevant terms:

Center: The point around which a circle is formed. All points on a circle's perimeter are the same distance from the circle's center.

Circumference: The distance around a circle.

Radius: A line segment that lies between the center of a circle and any point on the circle's perimeter

Diameter: A line segment that lies between two points on a circle's perimeter and runs through the circle's center. It is equal to two times the circle's radius.

Chord: A line segment that lies between two points on a circle's perimeter and does not run through the circle's center.

Secant: A line that intersects two points on a circle's perimeter.

Tangent: A line that intersects one point on a circle's perimeter.

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