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 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.



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