Question

Construct a cyclic quadrilateral EFGH where EF$=7$cm, EH$=4.8$cm, FH$=6.5$cm and EG$=6.6$cm.

Answer 1

$Step1:$ Draw a line segment $FE=7cm$

$Step2:$ With $F$ as centre and radius $6.5cm$ draw an arc.

$Step3:$ With $E$ as centre and radius $4.8cm$, draw another arc intersecting the previous arc at $H$.

$Step4:$ Join $FH$ and $EH$.

$Step5:$ Draw the perpendicular bisectors of $FE$ and $EH$ intersecting each other at $O$.

$Step6:$ With $O$ as centre and $OF(=OE=OH)$ as radius, draw the circumcircle of $△EFH$.

$Step71$ With $E$ as centre and radius $6.6cm$, draw an arc intersecting the circle at $G$.

$Step8:$ Join $FG$ and $GH$.

Thus, $EFGH$ is the required cyclic quadrilateral.