Question

Construct a cyclic quadrilateral PQRS such that PQ$=5.5$cm, QR$=4.5$cm, $\angle$QPR$={45}^o$ and PS$=3$cm.

Answer 1

$Step1:$ Draw a line segment $PQ=5.5cm$.

$Step2:$ Through $P$ draw $PX$ such that $\angle QPX={45}^0$

$Step3:$ With $Q$ as centre and radius $4.5cm$, draw an arc intersecting $QX$ at $R$ and join $QR$.

$Step4:$ Draw the perpendicular bisectors of $PQ$ and $QR$ intersecting each other at $O$.

$Step5:$ With $O$ as centre and $OP(=OQ=OR)$ as radius, draw the circumcircle of $△PQR$.

$Step6:$ With $P$ as centre and radius $3cm$, draw an arc intersecting the circle at $S$.

$Step7:$ Join $PS$ and $RS$.

Thus, $PQRS$ is the required cyclic quadrilateral.