Before revision:   The {\it Triangle Algorithm} (TA) computes p' \in conv(S) so that, either p'- p \leq \varepsilon R, R= \max \{ p -v : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).
After revision:  The {\it Triangle Algorithm} (TA)  p'- p \leq \varepsilon R, R= \max \{ p -v : v\in S\ {\it witness , i. e. the orthogonal bisector of pp' separates p from conv(S).