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:  CHM is not only a fundamental problem in Linear Programming, Computational Geometry, Machine Learning and Statistics, it also serves as a query problem in many applications e.g. Topic Modeling, LP Feasibility, Data Reduction. 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).