Question
Using ruler and compasses only, draw a right angle.
✓
Answer
Draw a ray $OA.$ With a convenient radius and centre at $O,$ draw an arc $PQ$ with the help of a compass intersecting the ray $OA$ at $P.$ With the same radius and centre at $P,$ draw another arc intersecting the arc $PQ$ at $R.$ With the same radius and centre at $R,$ draw an arc cutting the arc $PQ$ at $C,$ opposite $P.$ Taking $C$ and $R$ as the centre, draw two arcs of radius more than half of $CR$ that intersect each other at $S.$ Join $O$ and $S$ and extend the line to $B.$
$\angle\text{AOB}$ is the required angle of $90^\circ .$
$\angle\text{AOB}$ is the required angle of $90^\circ .$
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