A circle is the set of all points equidistant from a center point. The distance from the center to any point on the circle is the radius (r). The diameter (d = 2r) passes through the center. The circumference is C = 2πr = πd.
The area of a circle is A = πr². The value π ≈ 3.14159 represents the ratio of any circle's circumference to its diameter — this ratio is constant for all circles.
A radian is an angular measure based on the radius. One full revolution = 2π radians = 360°. To convert: degrees × (π/180) = radians.
Arc length is a fraction of the circumference: L = rθ (where θ is in radians). Sector area is A = ½r²θ. These formulas connect angle measurement to distance along the curve.