Construct a cyclic quadrilateral ABCD with AB = 7 cm, ∠A = 80°, AD = 4.5 cm and BC = 5 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 rough diagram and mark the measurements.

Step 2: Draw a line segment BA = 7cm.

Step 3: Through A draw AX such that ∠ BAX = 80°

Step 4: With A as centre and radius 4.5 cm, draw an arc intersecting AX at D and join AD.

Step 5: Draw the perpendicular bisectors of BA and AD intersecting each other at O.

Step 6: With O as centre and OA (=OB =OD ) as radius, draw the circumcircle of Δ ABD.

Step 7: With B as centre and radius 5 cm, draw an arc intersecting the circle at C.

Step 8: Join BC and CD.

Thus, ABCD is the required cyclic quadrilateral.