Draw an angle of 45° using scale and compasses only. Draw the bisector of this angle.
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 i.e. 45°
11. Now with centre B and radius more than half of BC, draw an arc.
12. With centre C and same radius draw another arc which cuts the previously drawn arc at X.
13. Join OX.
Therefore, OX is the bisector of ∠AOF.