Question

Construct a cyclic quadrilateral ABCD, where AB$=6.5$cm, $\angle$ABC$={110}^o$, BC$=5.5$cm and AB$||$CD.

Answer 1

$Step1:$ Draw a line segment $AB=6.5cm$.

$Step2:$ Through $B$ draw $BX$ such that $\angle ABX={110}^0$

$Step3:$ With $B$ as centre and radius $5.5cm$, draw an arc intersecting $BX$ at $C$.

$Step4:$ Draw the perpendicular bisectors of $AB$ and $BC$ intersecting each other at $O$.

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

$Step6:$ From $C$, draw $Cy$ such that $CY||AB$, which intersects the circle at $D$.

$Step7:$ Join $AD$

Thus, $ABCD$ is the required cyclic quadrilateral.