Arc/ Arc of a Circle

The arc of a circle is a portion of the circumference of a circle.

Arc

Image showing arc AB

The arc of a circle is a portion of the circumference of a circle. Measure an arc by two methods: 1) the measure of the central angle or Central arc in degrees 2) the length of the arc itself or central angle in radians

A practical way to determine the length of an arc in a circle is to plot two lines from the arc’s endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement:

Arc

OA = OB = R, AB = Length of the arc

 

 

Central angle in degrees:

 

measure of angle in degrees/360° = L/circumference.

Length of the arc = 2πR(C/360˚)

 

Central angle in radians:

Circumference of the circle = 2πR ;

π ≈ 3.142

C = Central angle = ∠AOB

Length of the arc = RC

 

Note: The 2π/360 converts the degrees to radians.

 

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