Question

Draw an angle ABC = 75°. Draw the locus of all the points equidistant from AB and BC.

Answer 1

Steps of construction:

1. Draw a ray BC.
2. Construct a ray RA making an angle of 75° with BC. Therefore, ABC = ABC = 75°
3. Draw the angle bisector BP of ∠ABC.
   BP is the required locus.
4. Take any point D on BP.
5. From D, draw DE ⊥ AB and DF ⊥ BC.
   Since D lies on the angle bisector BP of ∠ABC.
   D is equidistant from AB and BC.
   Hence, DE = DF
   Similarly, any point on BP is equidistant from AB and BC.
   Therefore, BP is the locus of all points which are equidistant from AB and BC.