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 segments AB = 6.5 cm
Step 2: Through B draw BX such that ∠ ABX = 110°
Step 3: With B as centre and radius 5.5 cm, draw an arc intersecting BX at C.
Step 4: Draw the perpendicular bisectors of AB and BC intersecting each other at O.
Step 5: With O as centre and OA (= OB = OC) as radius, draw the circumcircle of Δ ABC.
Step 6: From C, draw CY such that CY || AB, which intersects the circle at D.
Step 7: Join AD.
Thus, ABCD is the required cyclic quadrilateral.
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