Construct a cyclic quadrilateral KLMN such that KL = 5.5 cm, KM = 5 cm, LM = 4.2 cm and LN = 5.3 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 KL = 5.5 cm

Step 3: With K as centre and radius 5cm draw an arc.

Step 4: With L as centre and radius 4.2 cm, draw another arc intersecting the previous arc at M.

Step 5: Join KM and LM

Step 6: Draw the perpendicular bisectors of KL and LM intersecting each other at O.

Step 7: With O as centre and OK (=OL=OM ) as radius, draw the circumcircle of Δ KLM.

Step 8: With L as centre and radius 5.3 cm, draw an arc intersecting the circle at N.

Step 9: Join KN and MN.

Thus, KLMN is the required cyclic quadrilateral.