Construct a cyclic quadrilateral EFGH where EF = 7 cm, EH = 4.8 cm, FH = 6.5 cm and EG = 6.6 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 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.