Playing Kerbal Space Program, I found myself wondering about what a satellite would see of a planet depending on its field of view and its altitude. I tried attacking the problem from various angles but I always end up with a missing piece of information. 

Speaking a bit more formally, I have a circle **Planet** with a radius **r**. I have a point **Sat** which is at a distance **Orb** from the center of **Planet** (for our case, **Orb > r**). The line **Sat-Center(Planet)** bisects **A-Sat-B**, with **A** and **B** being points on the circle.

I know **Orb**, **r** and the angle **A-Sat-B**, what ways do I have to calculate **A-B**? (See below for a diagram.)

From there I think the [Circular segment](http://en.wikipedia.org/wiki/Circular_segment) will let me find the information I need but I'm stumped on the calculation.

![Planet-Sat diagram](https://i.stack.imgur.com/Uxrtx.png)