In geometry, a circle is a shape consisting of all points in a plane that are equidistant from a fixed center point. The distance from the center to any point on the circle is called the radius, denoted by 'r'. Circles have several important properties and formulas that can help us calculate various attributes.

One of the fundamental formulas related to circles is the circumference formula. The circumference of a circle can be calculated using the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159. For example, if a circle has a radius of 5 units, its circumference would be 2π(5) = 10π units.

Another important formula is the area of a circle, which is calculated using the formula A = πr^2. If we have a circle with a radius of 4 units, the area would be π(4^2) = 16π square units.