[math-fun] Problem for high school algebra ?

We have an _equilateral_ triangle in arbitrary position in standard 3D space with coordinate axes x,y,z. Translate this triangle (without rotations) so that its center becomes the origin. The 3 vertices are P1=(x1,y1,z1), P2=(x2,y2,z2), P3=(x3,y3,z3). We are given x1,y1,x2,y2 (but _not_ the z coordinates). Obviously, x3=-x1-x2, y3=-y1-y2, due to the center being the origin. Find a "simple" expression for the _radius_ of the circumcircle. This problem is trivial in the case that x1^2+y1^2 = x2^2+y2^2 = x2^2+y3^2 = R^2, in which case z1=z2=z3=0, so we are interested in the more difficult case. (Hint: you don't actually need the z coordinates.) (Yes, I do have an answer, which is simpler than I had expected.)