Question

Construct a cyclic quadrilateral ABCD when AB = 6.4 cm,$\angle ABX={45}^{\circ }$, AD = 4.8cm and AB || CD.

Answer 1

Given:

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

Construction:

(i) Draw a line segment AB = 6.4 cm.

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

(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.