The Comprehensive Guide To Circles: Properties, Equations, And Applications

Circle

A round plane figure whose boundary consists of points equidistant from the center.

A circle is a two-dimensional shape that is defined as a set of all points that are equidistant from a fixed point called the center.

Properties of a circle:

– The circle is symmetric about its center. That means that any line segment that passes through the center and intersects the circle will be bisected.
– The radius of the circle is the distance between any point on the circle and the center. All radii in a circle have the same length.
– The diameter of the circle is the distance between any two points on the circle that pass through the center. It is equal to twice the radius.
– The circumference of the circle is the distance around the perimeter of the circle. It is equal to 2π times the radius or π times the diameter.
– Circle equations can be written in several different forms, including the standard form (x – h)^2 + (y – k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Circles have important applications in many fields, including geometry, physics, engineering, architecture, and even art and design.

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