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 line segment FE = 7cm



Step 2: With F as centre and radius 6.5 cm draw an arc.



Step 3: With E as centre and radius 4.8 cm, draw another arc intersecting the previous arc at H.



Step 4: Join FH and EH.



Step 5: Draw the perpendicular bisectors of FE and EH intersecting each other at O.



Step 6: With O as centre and OF (= OE = OH ) as radius, draw the circumcircle of Δ EFH.



Step 7: With E as centre and radius 6.6cm, draw an arc intersecting the circle at G.



Step 8: Join FG and GH.



Thus, EFGH is the required cyclic quadrilateral.


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