Question
Construct an angle of 90° and bisect it.

Answer


Construction steps:
  1. Draw a line OA.
  2. Take a point B on OA. With B as the centre and any convenient radius, draw an arc cutting OA at M and N.
  3. With N as the centre and radius more than half of MN, draw an arc.
  4. With M as the centre and the same radius as before, draw another arc to cut the previous arc at W.
  5. Draw WB, meeting the arc at S. Produce it to C.
$\angle\text{ABC}$ is the required angle of 90° $\angle\text{ABC}$ is the required angle of 90°.
  1. With S as the centre and radius more than half of SN, draw an arc.
  2. With N as centre and the same radius as in step (6), draw another arc, cutting the previously drawn arc at point X.
  3. Draw BX and produce it to point D. Ray BD is the angle bisctor of $\angle\text{ABC}.$ Ray BD is the angle bisctor of $\angle\text{ABC}.$ Ray BD is the angl bisctor of $\angle\text{ABC}.$ Ray BD is the angle bisctor of $\angle\text{ABC}.$

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