Arc Length
Part of the Circles section of Coddy's Geometry journey. Lesson 16 of 62.
An arc is a piece of the circle between two points. The angle the two radii make at the center, the central angle, says how big a piece it is: out of the full turn of 360°, it takes its angle's share of the circumference.
Here the central angle is 60°, which is 60/360, one sixth of the turn. The whole circumference is 2 × π × 6 = 12π, so the arc is one sixth of that, 2π. As a rule, L = t/360 × 2πr, with t the central angle in degrees.
On the board, tap inside the slice between the two radii, choose the length of the arc, and pick Arc length.
Challenge
OA and OB are radii of circle O, and the central angle AOB is marked. Find the length L of the arc from A to B, exact in terms of π, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Circles
1Parts of a Circle
Center and RadiusChords and DiametersAll Radii Are EqualDiameter Is Two RadiiRecap: Parts of a Circle4Arcs and Sectors
Arc LengthArea of a SectorFind the Central AngleThe Missing Central AngleRecap: Arcs and Sectors2Circumference
Around the CircleUsing the DiameterRadius From CircumferenceCircumference With LettersRecap: Circumference5Radii Make Isosceles
Two Radii, One TriangleBase Angles From the CenterThe Angle at the CenterIsosceles With LettersRecap: Radii and Triangles8Angles on the Same Arc
Same Arc, Same AngleUsing the Same ArcSpot the Bow TieSame Arc With LettersRecap: Same Arc3Area of a Circle
The Area FormulaArea From the DiameterRadius From the AreaCircumference to AreaRecap: Area of a Circle6Inscribed Angles
Meet the Inscribed AngleHalf the Central AngleTwice the Inscribed AngleThe Big ArcInscribed With LettersRecap: Inscribed Angles