Question

Construct a cyclic quadrilateral ABCD when AB = 8 cm, BC = 6 cm, $\angle ABC={60}^{\circ }$ and AD = 5.4 cm.

Answer 1

In the cyclic quadrilateral ABCD, AB = 8 cm, BC = 6 cm, $\angle ABC={60}^{\circ }$ and AD = 5.4 cm.

Construction

(i) Draw a rough diagram and mark the measurements.

Draw a line segment AB = 8 cm.

(ii) Through B draw BX such that $\angle ABC={60}^{\circ }$.

(iii) With B as centre and radius 6 cm, draw an arc intersecting BX at C and join AC.

(iv) Draw the perpendicular bisectors of AB and BC intersecting each other at O.

(v) With O as centre and OA (= OB = OC) as radius, draw the circumcircle of $\Delta ABC$.

(vi) With A as centre and radius 5.4 cm, draw an arc intersecting the circle at D.

(vii) Join AD and CD.

(viii) Now, ABCD is the required cyclic quadrilateral.