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Option 2: Solve using arc length proportion

Formula for arc length in radians:

Arc length ≈  13.1 units
units
Step 1. Use the Arc Length Formula =




60/360 * diameter * π

Step 2. Calculate the diameter by multiplying the radius by 2
 radius * 2 = 9* 2 =18

Step 3. Simplify the fraction 60/360, and plug in your diameter                                
60/360 =1/6 * 18π

Step 4.  1/6 * 18π = 3π = 9.4285 units 

Arc length ≈ 9.4285 units


arc length formula
Step 1. Plug the information into the proportion. The arc length will become your variable.
arc length proportion central angle/360 =arc length/2pir
Step 2. Simplify 2(3.14)9 = 56.52
60/360=x/2(3.14)9
0/360 =x/56.52
Step 3. Cross multiply
360x= 3391.2

360/360 = 3391.2/360 =x
Step 4. Divide each side by 360
Arc length ≈ 9.42 units
4710/360 =13.1=60x/3
Step 4. Isolate x by dividing each side by 360
Step 3. Cross Multiply

360x= 4710
75/360 = x/62.82
Step 2. Simplify 2(3.14)10 = 62.8 and plug this in the arc length proportion.
or you can find arc length using a proportion.
arc length proportion central angle/360 =arc length/2pir
75/360 = x/2(3.14)10
Find the arc length of a circle with a central angle of 75 degrees and a radius of 10 units.

Step 1. Plug the information into the proportion. The arc length will become your variable.

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Common Core Standard    HSF-TF.A.1.

Finding the radius of a circle using arc length

The arc length formula can be used to calculate the radius of a circle. Basically you plug in the given information into the arc length formula, and solve for the radius. If the central angle is given in radians use: s = θ*radius
θ = measure of the central angle

If the central measure is in degrees use:
Measure central angle/360 =arc length/circumference (dπ)

Video: Using arc length to Find the radius of a circle.
Video Guide
0:53 Problem 1. Finding the radius of a circle in radians.
If an arc length measures 4π inches long, with a central angle of π/3, find the length of the radius.

2:00 Solution problem 1

2:16 Find the radius of a circle in degrees.
Given the arc length of 8π and a central angle of 120◦, find the radius.

4:29 Solution problem 2

Point of Reference
What is the length of an arc subtended by an angle of 7π/4 radians on a circle with a radius 10 units?

Step 1. Use the arc length formula for radians.   s = Θ *radius

Step 2. Plug in your given values    7π/4*10=17.5π  ≈54.97 units

measure of the central angle
θ
arc length formula
subtended angle
Subtended Angle
20
minor and major arc
Minor Arc
Major Arc
s = Θ *radius
Θ = measure of the central angle
Related sites on Arc length of a Circle

Arc Length and Radian Measure/Regents Prep  Short lesson covering arc length of a circle along with an explanation of degrees and radians, and several sample problems calculating arc measure.

Circles and Arcs/Khan Academy  A video,interactive sketchpad, and sample questions covering arcs of circles.

Arc Length Calculator   Check your homework with this calculator
arc length
s
θ
s
congruent angles of arcs
s
(The video works out the problem)
What is the length of the arc from A to B of a circle that has a central angle measure of  60 degrees and a radius of 9 units ?
Option One: Solve using the arc length formula:
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circumference of a circle
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In a circle congruent central angles will have congruent arcs and congruent arcs will have congruent central angles
The measure of an arc is equal to the measure of the central angle that intercepts the arc.

Example problems "Arc length of a circle"

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arc length outlined on circle
s
θ
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Finding Arc Length of a Circle

Finding the arc length explained
= diameter of the circle
  • Distance from A to B = the arc length.

  • Any two points on a circle except two points exactly opposite each other create a minor and major arc. 

  • The minor arc has a smaller angle measure and length than the major arc.
arc length of a circle graphic

Formula for arc length of a circle in degrees:

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The arc length of a circle is distance along the curved portion of a circle or any other curve. The arc length is longer than a chord which is a straight line distance between the endpoints. The circumference of a circle is considered an arc length with a measure of 360 degrees. A chord is defined as a straight line that intersects a circle at two points. The diameter of a circle is a chord that cuts a circle in half. The letter s is traditionally used to represent arc length. The s stands for subtends which means “opposite of.” A subtended angle is an angle created by an arc or any other object from a given point of view.