Question

Construct a cyclic quadrilateral ABCD with AB$=7$cm, $\angle$A$={80}^o$, AD$=4.5$cm and BC$=5$cm.

Answer 1

$Step1:$ Draw a line segment $BA=7cm$.

$Step2:$ Through $A$ draw $AX$ such that $\angle BAX={80}^0$

$Step3:$ With $A$ as centre and radius $4.5cm$, draw an arc intersecting $AX$ at $D$ and join $AD$.

$Step4:$ Draw the perpendicular bisectors of $BA$ and $AD$ intersecting each other at $O$.

$Step5:$ With $O$ as centre and $OA(=OB=OD)$ as radius, draw the circumcircle of $△ABD$.

$Step6:$ With $B$ as centre and radius $5cm$, draw an arc intersecting the circle at $C$.

$Step7:$ Join $BC$ and $CD$.

Thus, $ABCD$ is the required cyclic quadrilateral.