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?

kuhse4461a
2021-12-16
Answered

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?

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Jonathan Burroughs

Answered 2021-12-17
Author has **37** answers

There are 2 possible ways of finding length of AB

radius of circle (t)=8

AB= circumference$\times$ fraction of circle

$2\pi r\times \frac{1}{2\pi}=r=8$

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$AB=r=8$

radius of circle (t)=8

AB= circumference

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

Charles Benedict

Answered 2021-12-18
Author has **32** answers

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

$A(0,8)$ lies on the circle so $r=CA=8$

It is known from Geometry that if an circle AB of circle subtends an$\mathrm{\angle}$ of radian measure $\theta$ at the centre, then length of arc $AB=r\theta$

In our case$r=8$ and $\theta =1$ radian

The length of arc$AB=8$

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

In our case

The length of arc

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