Before revision:  We show that it is NP-complete to decide whether a given edge can be inserted into a simple drawing , by this solving an open question by Arroyo, Derka, and Parada and a pseudosegment \sigma, it can be decided in polynomial time whether there exists a pseudocircle \Phi_\sigma extending \sigma for which \mathcal{A}\cup\{\Phi_\sigma\} is again an arrangement of pseudocircles} .
After revision:  We show that it is NP -complete to decide whether a given edge can be inserted into a simple drawing , by this solving an open question by Arroyo, Derka, and Parada and a pseudosegment \sigma, it can be decided in polynomial time whether there exists a pseudocircle \Phi_\sigma extending \sigma for which \mathcal{A}\cup\{\Phi_\sigma\} is again an arrangement of pseudocircles} .