$A_{\mathrm{\infty }}$ implies NTA for a class of variable coefficient elliptic operators

We consider a certain class of second order, variable coefficient divergence form elliptic operators, in a uniform domain $\mathrm{\Omega }$ with Ahlfors regular boundary, and we show that the $A_{\mathrm{\infty }}$ property of the elliptic measure associated to any such operator and its transpose imply that the domain is in fact NTA (and hence chord-arc). The converse was already known, and follows from work of Kenig and Pipher.