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.
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