Calculating Angle ACB in a Circle Given Point B and Angle from Point A

[JonasB]

Hello all,
sorry if this is a trivial question, or if it's been asked before, but I'm not good with math terminology so my googling doesn't give me much info.. I'm trying to work out a problem in order to recreate some functions that are missing from the public API of Google Earth. (If this is solved I'll post the results for the benefit of other GE users)

I have circle, with a known radius (center called C), and a point B outside a circle at a known distance. I also have a known angle from the point which projects at some point A on the circle's circumference. How can I calculate the angle ACB, i.e. the angle between the circle's center to B and the circle's center to A?

I (hope I've managed to) upload an image describing the problem.

Thanks a lot,
Jonas

 

[ice109]

what do you mean by projects?

 

[Sesse]

what do you mean by projects?

I think he means a line that connects B to A.

In that case, from what I understand you know the length of CB(given) and CA(radius of the circle). You know the angle CBA(given) as well. Using law of cosines, you can find the length of the other side, BA. Then using law of cosines again, you can calculate the angle you need.

 

[JonasB]

I think he means a line that connects B to A.

In that case, from what I understand you know the length of CB(given) and CA(radius of the circle). You know the angle CBA(given) as well. Using law of cosines, you can find the length of the other side, BA. Then using law of cosines again, you can calculate the angle you need.

I found this:
Math.Asin(side2 * Math.Sin(angle1) / side1)
which, according to the description, should give me the CAB angle. I don't see why exactly, but I'm happy as long as it works. Thanks anyway!
/Jonas