Construct a cyclic quadrilateral ABCD where AB = 6 cm, AD = 4.8 cm, BD = 8 cm and CD = 5.5 cm.

We need to construct the required quadrilateral, when three sides and one diagonal of a cyclic quadrilateral are given.

Steps of construction:

Step 1: Draw a rough diagram and mark the measurements.

Step 2: Draw a line segment DA = 4.8 cm.

Step 3: With D and A as centres, draw arc with radii 8 cm and 6 cm respectively, to intersect at B. join AB and DB.

Step 4: Draw the perpendicular bisectors of DA and AB intersect at O.

Step 5: With O as the centre and OD (=OA=OB ) as radius draw the circumcircle of Δ ABD

Step 6: With d as the centre and radius 5.5 cm. draw an arc intersecting the circumcircle at C.

Step 7: Join DC and BC.

Step 8: ABCD is the required cyclic quadrilateral.