Using normalized barycentric coordinates, the authors prove four elegant inequalities with parameter about a point and its distances from the vertices and sides of a triangle. The proof relies on showing the positivity of a certain polynomial in six variables \(f_1(a,b,c,x,y,z)\), with \(a\), \(b\), \(c\) the sides and \(x\), \(y\), \(z\) the barycentric coordinates of the point. It is far too complex for any human to do the calculation, but it is not mentioned in the paper which case is used in the proof.