Let us do it python school... because you can do it directly as a spreadsheet or you can use Numpyarrayto featureclass or the insertcursor approach to produce your geometries after the calculations are done. Verbose description.
Do it in reverse first
import numpy as np
np.set_printoptions(edgeitems=5,linewidth=80,precision=4,suppress=True,threshold=10)
cent = np.array([0,0],dtype="float64")
pnts = np.array([[1,1],[1,2],[-3,3],[-4,-4],[5,-5]],dtype="float64")
Xs = pnts[:,0]
Ys = pnts[:,1]
diff = pnts-cent
angles= np.degrees(np.arctan2(diff[:,1],diff[:,0]))
dist = np.hypot(diff[:,0],diff[:,1])
data = np.vstack((Xs,Ys,angles,dist)).T
print("Origin (0,0)\n {:<10s} {:<10s} {:<10s} {:<10s}".format("Xs","Ys","angles","dist"))
print("{}".format(data))
Origin (0,0)
Xs Ys angles dist
[[ 1. 1. 45. 1.4142]
[ 1. 2. 63.4349 2.2361]
[ -3. 3. 135. 4.2426]
[ -4. -4. -135. 5.6569]
[ 5. -5. -45. 7.0711]]
Now lets do it forward
angles= np.degrees(np.arctan2(diff[:,1],diff[:,0]))
dist = np.hypot(diff[:,0],diff[:,1])
rads = np.deg2rad(angles)
sines = np.sin(rads)
coses = np.cos(rads)
Xn = sines * dist
Yn = coses * dist
data = np.vstack((angles,dist,Xs,Ys)).T
print("Origin (0,0)\n {:<10s} {:<10s} {:<10s} {:<10s}".format("angles","dist","Xn","Yn"))
print("{}".format(data))
Origin (0,0)
angles dist Xn Yn
[[ 45. 1.4142 1. 1. ]
[ 63.4349 2.2361 1. 2. ]
[ 135. 4.2426 -3. 3. ]
[-135. 5.6569 -4. -4. ]
[ -45. 7.0711 5. -5. ]]
if you can assemble the origin point and all the destination points together into one file, you can then steal the code from the following line to generate your polylines or simply use the toolbox to generate desire lines connect the destinations to the origins
http://www.arcgis.com/home/item.html?id=6ce9db93533345e49350d30a07fc913a
Or there is Bearing Distance To Line—Help | ArcGIS for Desktop which can be use on or better still
XY To Line—Help | ArcGIS for Desktop
generate this....
final from Xc,Yc,Xs,Ys
[[ 0. 0. 1. 1.]
[ 0. 0. 1. 2.]
[ 0. 0. -3. 3.]
[ 0. 0. -4. -4.]
[ 0. 0. 5. -5.]]
from this...
N = len(Xs)
Xc = np.empty(N)
Xc.fill(0.)
Yc = np.empty(N)
Yc.fill(0.)
pairs = np.array(list(zip(Xc,Yc,Xs,Ys)))
print("final from Xc,Yc,Xs,Ys\n{}".format(pairs))