Question

Construct a cyclic quadrilateral PQRS, with PQ$=6.5$cm, QR$=5.5$cm, PR$=7$cm and PS$=4.5$cm.

Answer 1

$Step1:$ Draw a line segment $PQ=6.5cm$

$Step2:$ With $P$ and $Q$ as centres, draw arc with radii $7cm$ and $5.5cm$ respectively, to intersect at $R.$ Join $PR$ and $QR$.

$Step3:$ Draw the perpendicular bisectors of $PQ$ and $QR$ intersect at $O$.

$Step4:$ With $O$ as centre and $OP(=OQ=OR)$ as radius, draw the circumcircle of $△PQR$.

$Step5$ With $P$ as centre and radius $4.5cm$, draw an arc intersecting the circle at $S$.

$Step6:$ Join $PS$ and $RS$.

$Step8:$ $PQRS$ is the required cyclic quadrilateral.

Hence, this is the answer.