Question

Construct a cyclic quadrilateral PQRS given PQ$=5$cm, QR$=4$cm, $\angle$QPR$={35}^o$ and $\angle$PRS$={70}^o$.

Answer 1

$Step1:$ Draw a line segment $PQ=5cm$.

$Step2:$ Through $P$ draw $PX$ such that $\angle QPX={35}^0$

$Step3:$ With $Q$ as centre and radius $4cm$, draw an arc intersecting $PX$ 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 $△PQR$.

$Step6:$ From $R$, draw $RY$ such that $\angle PRS={70}^0$, which intersects the circle at $S$.

$Step7:$ Join $PS$

Thus, $PQRS$ is the required cyclic quadrilateral.