Construct a cyclic quadrilateral ABCD, where AB = 6.5 cm, ABC = 110°, BC = 5.5 cm and AB || CD.

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.