Question

A Circle centered at 0,0 includes 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
A. 8
B. 4pi
C. 16
D. 8pi

Answer 1

We know that
the equation of a circle is
(x-h)²+(y-k)²=r²
where 
(h,k) is the center
and r is the radius
in this problem (h,k) is (0,0)
so the equation is
x²+y²=r²

step 1
find the radius 
substitute the point a (0,8) in the equation
0²+8²=r²------> r=8

step 2

find the circumference
C=2*pi*r-----> C=2*pi*8----> C=16*pi units

if 2*pi radians (full circle) has a length of--------------> 16*pi
  1 radians--------------------------> x
x=16*pi/(2*pi)-----> 8  units

the answer is the option
A) 8