Question

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

Answer 1

Construction:
1. Draw a $\Delta PQR$ with given measurement.
2. Draw a bisectors of the side $PQ$ and $QR$ which meet at $O$.
3. Draw a circle with centre $O$ and radius $OP$.
4. Draw a line $RY$ such that $\angle PRY={70}^o$ which meet the circle at $S$.
5. Join $RS$ and $PS$.
6. $PQRS$ is a required cyclic quadrilateral.