Given three vectors $u,v,w \in S^2$ and the triangle $[u,v,w]$ I want to find its circumscribed circle. However, I don't know how to approach this problem. Would some one please explain?
In my understanding, one needs to somehow find the altitudes of the spherical triangle and then the point of its intersection (circumcentre)? Then what about the radius?
The three points lie on a plane, which cuts the sphere in a circle. That is the circumscribed circle.
To calculate its radius, calculate the distance $d$ of the plane from the center of the sphere. If the sphere has radius $1$, then the radius of the circumcircle is $\arccos{(d)}$.