lines of bearing bounding a circle diagram
Given a circle of radius R, that is D units from the origin, I would like to find a method for finding the two lines of bearing from the origin that are tangent to to the circle.
This is not a homework assignment. I don't want the answer spelled out, I'd rather be pointed in the direction of it, such as what formulas to use; I don't even know where to start. In fact, the more vague your answer is, the better it will probably be.
In case it helps to explain, use the following values in examples: R = 1, D = 10; but I would like to find a general algorithm that will work for a circle of any arbitrary size and distance from the origin (and it doesn't have to be in the first quadrant, that was just to keep the image size down).
I was unable to find a similar question using search, but apologies in advance if this has been asked before. I'll close the question right away if it has.

Take a circle $\Gamma'$ whose diameter is given by the origin and the centre of your circle $\Gamma$. 
The intersections between $\Gamma$ and $\Gamma'$ give the points of tangency: can you prove why? 
