Before revision:  \etal As a second application of our technique, we again have three n-point sets A, B, and C in the plane, and we want to determine whether there exists a triple (a,b,c) \in A\times B\times C that simultaneously satisfies two  real polynomial equations.
After revision:  \etal As a second application of our technique, we again have three n-point sets A, B, and C in the plane, and we want to determine whether there exists a triple (a,b,c) \in A\times B\times C that simultaneously satisfies two independent real polynomial equations.