Question

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

Answer 1

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 = $2 \pi r\frac{\theta}{360}$

Now,

Along the arc ABC, ∠APC = ∠APB+∠BPC

or, ∠APC = 111°+129°

or, ∠APC =240°

Taking,

r = 6, θ = 240° we get,

$arc length ABC = 2\pi (6)\frac{240}{360}$

or, $arclength ABC = 8 \pi$

Hence,

The length of the arc ABC is 8π.