# The Geometry of Circles

Definitions and formulas for the radius of a circle, the diameter of a circle, the circumference (perimeter) of a circle, the area of a circle, the chord of a circle, arc and the arc length of a circle, sector and the area of the sector of a circle
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 radius of a circle diameter of a circle circumference of a circle area of a circle chord of a circle arc of a circle arc length of a circle sector of a circle area of a sector of a circle

 The radius of a circle: The radius of a circle is the distance from the center of the circle to the outside edge.
 The diameter of a circle: The diameter of a circle is longest distance across a circle.  (The diameter cuts through the center of the circle.  This is what makes it the longest distance.)
 The circumference of a circle (the perimeter of a circle): The circumference of a circle is the perimeter -- the distance around the outer edge.Circumference = where r = the radius of the circleand pi = 3.141592...
 The area of a circle: Area = where r = the radius of the circleand pi = 3.141592...
 A chord of a circle: A chord of a circle is a line segment that connects one point on the edge of the circle with another point on the circle.(The diameter is a chord -- it's just the longest chord!)

 An arc of a circle: An arc of a circle is a segment of the circumference of the circle.
 The formula for the arc length of a circle: Arc length of a circle in radians:Arc Length =  Arc length of a circle in degrees: Arc Length =
 A sector of a circle: A sector of a circle is a pie shaped portion of the area of the circle.  Technically, the piece of pie is between two segments coming out of the center of the circle.
 The area of a sector of a circle: Sector area of a circle in radians:Sector Area =  Sector area of a circle in degrees: Sector Area =