 # A circle centered at (0, 0) includes the point A(0, 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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There are 2 possible ways of finding length of AB
AB= circumference$×$ fraction of circle
$2\pi r×\frac{1}{2\pi }=r=8$
an angle subtendet at the centre of 1 radian occurs when the arc length is equal to the radius
thus when $AB=r=8$
###### Not exactly what you’re looking for? Charles Benedict
Let the centre and radius be C(0,0) and r, resp
$A\left(0,8\right)$ 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 $AB=8$