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 -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 -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? -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-

1. Chapter 3 Class 11 Trigonometric Functions (Term 2)
2. Concept wise
3. Arc length

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