Said best with a picture. Given angles a and b, solve for angle x. (Note that the top right vertex is also the center of the circle)
What I've tried
Unable to find a simple method to get to x, I decided to draw all chords, and extend all segments to the edges of the triangle:
I've managed to get just about every angle except the few I need to find x, so I'm not sure if this method of extending all lines has helped. Here's how far I got (excuse the rearrangement, I needed room to write):
I think I'm overlooking something simple here. I'm not asking for the solution necessarily, just how I should get there.
Also if someone could help me with a more technically descriptive title, I would love an edit.