if we have 3 points (all having +ve co-ordinates(>=0)) in X-Y co-ordinate system, then how can we find the co-ordinates of intesection of lines of minimum lenght which connect them?

I thought it could be the centroid of the trinagle formed by these point but it doesn't seem so . Can there be any other such property?

E.g for points (2,2) ,(1,1) and (2,1) , the requied point is

1.788675 1.211324

Thanks.