Question

Construct a cyclic quadrilateral ABCD in which AB = 8cm, AC = 9 cm, BC = 7 cm, and AD = 5.4 cm.

Answer 1

In the cyclic quadrilateral ABCD, AB = 8 cm, AC = 9 cm.

BC = 7 cm, and AD = 5.4 cm.

Steps of construction:

(i) Draw a rough diagram and mark the measurements.Draw a line segment AB = 8 cm.

(ii) With A and B as centres, draw arcs with radii 9 cm and 7 cm respectively, to intersect

at C. Join AC and BC.

(iii) Draw the perpendicular bisectors of AB and BC to intersect at O.

(iv) With O as the centre and OA (= OB = OC) as radius draw the circumcircle of ∆ ABC

(v) With A as the centre and radius 5.4 cm. draw an arc intersecting the circumcircle at D.

(vi) Join AD and CD.

Now, ABCD is the required cyclic quadrilateral.