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 = 

The area of a circle:  
Area = 

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 = 