I'm back, wow, twice a day nowadays. I need to calculate circumcenter coordinates (or at least I hope they're called that) at point C for an isosceles triangle (the circle must be such, that created triangle is). I know the point O (origin), two vectors p and q (length may differ) originating in that point (leading to points P and Q). I also know the radius r of this to be circumscribed circle. When the circle's center is known it should create said green highlighted isosceles triangle. Here is drawing for better understanding:
Best Answer
Let $\mathbf{p}^0,\mathbf{q}^0$ denote the vectors $\mathbf{p},\mathbf{q}$ normalized to unit length. As the triangle is to be isosceles, $\mathbf{C}$ lies on the ray bisecting the rays $\mathbf{OP}$ and $\mathbf{OQ}$. The direction of that ray can be computed as $$\mathbf{v} = (\mathbf{p}^0+\mathbf{q}^0)^0$$ With $r$ given, you know that $\mathbf{C}$ is located precisely $r\mathbf{v}$ from $\mathbf{O}$.