Cool math .com - The Geometry of Circles - Radius, Diameter, Circumference, Area, Arc Length, Area of a Sector

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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

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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 circle and pi = 3.141592...

The area of a circle:
	Area = where r = the radius of the circle and 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:

circle graphic

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:

circle graphic

Sector area of a circle in radians:

Sector Area =

Sector area of a circle in degrees:

Sector Area =