To solve this problem, use the fact that 2 diagonals of a parallelogram bisect each other.
Mark point A, and from A, draw a horizontal ray rightwards. Mark point B on the ray exactly 4.6cm away from A. Draw 2 arcs above AB: one from A with radius 2.1cm (=½·AC), and the other from B with radius 2.9cm (=½·BD), and mark the crossing of 2 arcs O.
Extend AO and BO upwards. From O, draw 2 arcs: one with radius OA (=½·AC) crossing the extension of AO at C, and the other with radius OB (=½·BD) crossing the extension of BO at D. Connect B to C, C to D and D to A.
Check if AB=CD and BC=DA. CKD. Therefore quadrilateral ABCD is the required parallelogram, and BC=approx. 2.12cm