I'm given one of the vertices of a regular tetrahedron and the radius of the circumsphere. I also know the center point of the circumsphere. How can I find the remaining three vertices? (It was pointed out in the comments that "given any solution, you can rotate it around the line through the given vertex and the circumcentre." I think this doesn't matter since any possible solution will work for my application).
So far I've mostly just tried guessing. I'm working on an OpenGL program and I need to draw a regular tetrahedron algorithmically. I don't have much of a math background so I'm a bit lost on even where to begin on this.