Let us consider a circle with radius r

Length of Arc Formula.jpg

 

Arc is a portion of the circle.

 

Let the arc subtend angle θ at the center

Then,

Angle at center = Length of Arc/ Radius of circle

θ = l/r

 

Note: Here angle is in radians.

Let’s take some examples

If radius of circle is 5 cm, and length of arc is 12 cm. Find angle subtended by arc

Length of an arc formula - Part 2

-a-

Given radius = r = 5 cm

Length of arc = l = 12 cm

We know that

  θ = l /r

  θ = 12/5

∴ Angle subtended by angle arc = 12/5 radians

-ea-

 

If angle subtended by arc is 1 radian, and radius of circle is 1 cm. Find length of arc

Length of an arc formula - Part 3

-a-

Given radius = r = 1 cm

Angle = θ = 1 radian

 

We know that

  θ = l /r

  1 = l /1

  1 = l

  l = 1 cm

 

∴ Length of the arc = 1 cm

-ea-

 

If angle subtended by arc is π radian, and length of the arc is 2 π cm. What is the radius of circle?

Length of an arc formula - Part 4

-a-

Given

Length of arc = l = 2π cm

Angle = θ = π radian

 

We know that

  θ = l /r

   π = 2π/r

  r = 2π/π

  r = 2 cm

 

∴ Radius of circle = 2 cm

-ea-

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Transcript

Let us consider a circle with radius r Arc is a portion of the circle. Let the arc subtend angle θ at the center Then, Angle at center = Length of Arc/ Radius of circle θ = l/r Note: Here angle is in radians. Let’s take some examples If radius of circle is 5 cm, and length of arc is 12 cm. Find angle subtended by arc Given radius = r = 5 cm Length of arc = l = 12 cm We know that θ = l/r θ = 12/5 ∴ Angle subtended by angle arc = 12/5 radians If angle subtended by arc is 1 radian, and radius of circle is 1 cm. Find length of arc Given radius = r = 1 cm Angle = θ = 1 radian We know that θ = l/r 1 = l/1 1 = l l = 1 cm ∴ Length of the arc = 1 cm If angle subtended by arc is π radian, and length of the arc is 2π cm. What is the radius of circle? Given Length of arc = l = 2π cm Angle = θ = π radian We know that θ = l/r π = 2π/r r = 2π/π r = 2 cm ∴ Radius of circle = 2 cm

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo