Question

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

Answer 1

Given, $PQ=5.5$ cm
$QR=4.5$ cm
$\angle QPR={45}^o$
$PS=3$ cm
Construction:
(1) Draw a line segment $PQ=5.5$ cm
(2) Through $P$ draw $PX$ such that $\angle QPX={45}^o$
(3) With $Q$ as the centre and radius $4.5$ cm, draw an arc intersecting $PX$ and join $RQ$
(4) Draw the perpendicular bisector and $QR$ intersecting at $O$.
(5) $O$ as the centre draw a circumcircle with radius $OP$
(6) Draw an arc $3$ cm with centre $P$ on the circumcircle.
(7) Join $PS,SR$
(8) $PQRS$ is the required cyclic quadrilateral.