Question: "A circle centered at (0, 0) includes the..."

kuhse4461a

Answered question

2021-12-16

A circle centered at (0, 0) includes the point A(0, 8). Point B lies on the circle such that the center angle with endpoints A and B measures 1 radian. What is the length of AB?

Answer & Explanation

Jonathan Burroughs

Beginner2021-12-17Added 37 answers

There are 2 possible ways of finding length of AB
radius of circle (t)=8
AB= circumference

\times

fraction of circle

2 π r \times \frac{1}{2 π} = r = 8

definition of 1 radian
an angle subtendet at the centre of 1 radian occurs when the arc length is equal to the radius
thus when

A B = r = 8

Charles Benedict

Beginner2021-12-18Added 32 answers

Let the centre and radius be C(0,0) and r, resp

A (0, 8)

lies on the circle so

r = C A = 8

It is known from Geometry that if an circle AB of circle subtends an

∠

of radian measure

θ

at the centre, then length of arc

A B = r θ

In our case

r = 8

and

θ = 1

radian
The length of arc

A B = 8

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Didn't find what you were looking for?