Can Trilateration Determine the Angle in a Dynamic Circle Problem?

[lzh]

This math problem is something I made in trying to test a theory. I'm not too sure if it can be solved, can someone try to solve this?
I have a central point(star) and an circle. The point is fixed in position, but the circle is free moving and moves without direction. The circle constantly adjusts its radius to fit the point on its edge(on the boundary of the circle). No matter what, the radius of the circle is always known.
How can the location of the central point relative from the center of circle be determined?
Find the angle between the line formed between the central point and center of circle and the horizontal line(dashed green line on fig).

Trilateration determines the central point quite easily. However, it's the angle that's hard to determine. I need a equation that can solve for the angle with only the radius of three circles.
points 1,2,3 are the center of the circle at one second intervals.
http://img228.imageshack.us/my.php?image=cirwh9.gif

Does anyone know how to do this?
Any help is appreciated!

EDIT: Please note that the position of the central point(the star) is not known. You have to use trilateration to find it.

 

[lzh]

it seems like the problem cannot be solved because the circle's position is infinitely many.

But what if instead of one circle, there are two? Both circles will always be a fixed distance from each other and the center of the second circle is right behind the first(looking from above). Any inputs?

 

[lzh]

after some modification of the scenario-using three circles that are always the same distance from each other, I have managed to solve the problem.