Question

Construct a cyclic quadrilateral ABCD when $AB=5.8$cm, $\angle$ABD$={35}^o$, AD$=4.2$cm and AB$||$CD.

Answer 1

Given: In the cyclic quadrilateral ABCD, AB$=5.8$cm, $\angle$ABD$={35}^o$, AD$=4.2$cm and AB$||$CD.

Construction:

(i) Draw a rough diagram and mark the measurements. Draw a line segment AB$=5.8$cm.

(ii) From B, draw BX such that $\angle$ABX$={35}^o$.

(iii) With A as centre and radius $4.2$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(=)B=OD) as radius, draw a circumcircle of $\Delta$ABD.

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

Join BC.

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