Using ruler and compasses, construct a parallelogram ABCD given that AB = 4 cm, AC = 10 cm, BD = 6 cm. Measure BC.

Steps of construction:

1. Draw a line segment AB = 4 cm.
2. Construct triangle OAB such that
   OA = $\dfrac{1}{2}$ x AC = 5cm
   OB = $\dfrac{1}{2}$ x BD = 3cm
   With A as center and radius 5 cm and with centre B and radius 3 cm, draw arcs intersecting each other at O.
   As, diagonals of || gm bisect each other.
3. Produce AO to C such that OA = OC = 5cm.
4. Produce BO to D such that OB = OD = 3cm.
5. Join AD, BC and CD. Then ABCD is the required parallelogram.

On measuring, BC = 7.2 cm.

Hence, BC = 7.2 cm.