Construct a cyclic quadrilateral ABCD, given AB = 6 cm, ∠ABC = 70°, BC = 5 cm 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 = 6 cm.

Step 2: Through A draw BX such that ∠ ABX = 70°

Step 3: With B as centre and radius 5 cm, draw an arc intersecting BX at C and join BC.

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 ∠ ACD =30° , which intersects the circle at D.

Step 7: Join AD.

Thus, ABCD is the required cyclic quadrilateral.