Question

In the figure below the radius of circle p is 6 units.​

Answer 1

The length of the arc ABC is 25.12 units

To determine the length of the arc, we make use of the formula,

Length of an Arc = θ × (π/180) × r,

where;

• θ is in degree.
• r is the radius

Now, we have from the diagram that;

The angle measure, θ = 111 + 129

add the values, we get;

θ = 240 degrees

Substitute the value

Length of ABC = 240 × 3.14/180 ×6

Multiply the values, we get;

Length of ABC =25.12 units

Answer 2

Given:

The radius of the given circle = 6 unit

P be its center.

Along the arc AB, ∠APB = 111°

Along the arc BC, ∠BPC = 129°

To find the length of the arc ABC.

Formula

The relation between arc length, θ, r as radius is

arc length =
`2 \pi r(\theta)/(360)`

Now,

Along the arc ABC, ∠APC = ∠APB+∠BPC

or, ∠APC = 111°+129°

or, ∠APC =240°

Taking,

r = 6, θ = 240° we get,

`arc length ABC = 2\pi (6)(240)/(360)`

or,
`arclength ABC = 8 \pi`

Hence,

The length of the arc ABC is 8π.