Dubins showed that any shortest path of a car-like robot consists of exactly three path segment which are either arcs of circles of radius r(denoted C), or straight line segments(denoted S). Possible six types classified into two families, i.e. CSC and CCC. CSC includes 2 types(LRL and RLR) and CSC includes 4 types(LSL, RSR, LSR, RSL). This paper proposes new formulae for CSC family to find the shortest smooth path between the initial and final configurations of a car-like robot. The formulae is used for finding connection points explicitly between ClongrightarrowS and SlongrightarrowC which are necessary for real applications. The formulae have simple forms mainly because they are transformed into origin of their original coordinates of initial and target configuration, and derived from a standard forms which are a representative configuration of LSL and LSR type respectively. The proposed formulae, which are derived from the standard forms, are simple and new method.