# Centre of a spherical triangle

Suppose I have a triangle defined by 3 unit vectors {$v_1, v_2, v_3$} in a 3 dimensional complex inner product space.

What would be the centre of such a triangle? I guess it should be something like $(v_1+v_2+v_3)/3$.

How about if the 3 vectors define a spherical triangle on the unit sphere? Is it just a case of taking the vector in the paragraph above and projecting it onto the unit sphere? Are there any other possible candidates which I imagine may make use of the inner products of the 3 vectors?

@HagenvonEitzen. So say I wanted to calculate the center of the inscribed circle. Would this then be $[|v_2-v_3|v_1+|v_1-v_3|v_2+|v_2-v_1|v_3]$ (normalised to ensure it lies on the unit sphere)? Would I be right in thinking that projecting back through the origin would give the center for the other spherical triangle that's been defined? –  Stan Jan 22 '13 at 13:57