Question

Construct a cyclic quadrilateral ABCD when AB$=6$cm, BC$=5.5$cm, $\angle$ABC$={80}^o$ and AD$=4.5$cm.

Answer 1

Given: In the Cyclic Quadrilateral ABCD, AB$=6$cm, BC$=5.5$cm, $\angle$ABC$={80}^o$ and AD$=4.5$cm.
Construction:
(i) Draw a rough diagram and mark the measurements. Draw a line segment AB$=6$cm.
(ii) Through B draw BX such that $\angle$ABX$={80}^o$.
(iii) With B as centre and radius $5.5$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 $4.5$cm, draw an arc intersecting the circle at D.
(vii) Join AD and CD.
(viii) Now, ABCD is the required cyclic quadrilateral.