Question

Draw a circle of radius $6cm.$ Draw a tangent to this circle making an angle of ${30}^o$ with a line passing through the centre.

Answer 1

Steps of construction

$STEPI$
Draw a circle with centre $O$ and radius $3cm$.

$STEPII$
Draw a radius $OA$ of this circle and produce it to $B$.

$STEPIII$
Construct an angle $\angle AOP$ equal to the complement of ${30}^o$ i.e. equal to ${60}^o$.

$STEPIV$
Draw perpendicular to $OP$ at $P$ which intersects $OA$ produced at $Q$

Clearly, $PQ$ is the desired tangent such that $\angle OQP={30}^o$