Construct an angle of 90° and draw its bisector.

Steps of Construction

1. Draw a line segment OA.

2. With O as the centre and any suitable radius draw an arc, cutting OA at B.

3. With B as the centre and the same radius cut the previously drawn arc at C.

4. With C as the centre and the same radius cut the arc at D

5. With C as the centre and the radius more than half CD draw an arc.

6. With D as the centre and the same radius draw another arc which cuts the previous arc at E.

7. Join E. So ∠AOE=90°

8. Now with B as centre and radius more than half of CB draw an arc.

9. With C as the centre and same radius draw an arc which cuts the previous at F.

10. Join OF. Therefore, it is the bisector of the right ∠AOE.