Construct a cyclic quadrilateral ABCD such that AB = 5.5 cm ∠ABC = 50°, ∠BAC = 60° and ∠ACD = 30°

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 AB = 5.5 cm

Step 2: Through A draw AX such that ∠ BAX = 60°

Step 3: Through b draw BY such that ∠ ABY = 50°

Step 4: Mark the point where BY meets AX and label it as C.

Step 5: Draw the perpendicular bisectors of AB and BC intersecting each other at O.

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

Step 7: From A, draw AZ such that ∠ BAZ = 80° , which intersects the circle at D.

Step 8: Join AD and CD.

Thus, ABCD is the required cyclic quadrilateral.