Answer :

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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