Acircle 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

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

(in the image)

Step-by-step explanation:

for the slope one - both triangle a and b have a slope of 5/3 (b's goes from 15/9 to 5/3 because of simplifying)

for the second one - 5/3=15/9 because the sides of both triangles correspond