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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:

circle graphic

The radius of a circle is the distance from the center of the circle to the outside edge.

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The diameter of a circle:

circle graphic

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.)

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The circumference of a circle (the perimeter of a circle):

circle graphic

The circumference of a circle is the perimeter -- the distance around the outer edge.

Circumference = circle graphic
where r = the radius of the circle
and pi = 3.141592...

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The area of a circle:

circle graphic

Area = circle graphic
where r = the radius of the circle
and pi = 3.141592...

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A chord of a circle:

circle graphic

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!)

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An arc of a circle:

circle graphic

An arc of a circle is a segment of the circumference of the circle.

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The formula for the arc length of a circle:

circle graphic

Arc length of a circle in radians:

Arc Length circle graphic

Arc length of a circle in degrees:

Arc Length circle graphic

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A sector of a circle:

circle graphic

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.

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The area of a sector of a circle:

circle graphic

Sector area of a circle in radians:

Sector Area circle graphic

Sector area of a circle in degrees:

Sector Area circle graphic