Curvature continuity

You cannot have curvature continuity (which is G2, not c2) between to arcs unless the arcs have the same curvature (radius) and share centers, in which case - they make up one arc.

If you can make a gap between the arcs and use a spline (curve through points) you can use just the arc end points and add the G2 continuity.

Or, you can make an approximate spline and select your two arcs. The result will be one spline curve that follows your arcs very closely.