Question

Construct a cyclic quadrilateral ABCD when AB = 7.6 cm, $\angle ABD={30}^{\circ }$, AD = 5.4cm and AB || CD.

Answer 1

Given: In the cyclic quadrilateral ABCD, AB = 6.4 cm, $\angle ABD={45}^{\circ }$, AD = 4.8 cm and AB || CD.

Construction:

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

Draw a line segment AB = 6.4 cm.

(ii) From B, draw BX such that $\angle ABD={45}^{\circ }$.

(iii) With A as centre and radius 4.8 cm, draw an arc intersecting BX at D.

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

(v) With O as centre, and OA (= OB = OD) as radius, draw a circumcircle of DABD.

(vi) Draw DY such that DY || AB intersecting the circle at C.

Join BC.

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