Question

Using a ruler and a compass, construct a triangle ABC in which AB = 7 cm, ∠CAB = 60° and AC = 5 cm. Construct the locus of :

1. points equidistant from AB and AC.
2. points equidistant from BA and BC.
   Hence construct a circle touching the three sides of the triangle internally.

Answer 1

Steps of construction:

1. Draw a line AB = 7 cm.
2. Taking P ascentre and same radius, draw an arc of a circle which intersects AB at M.
3. Taking M ascentre and with the same radius as before drawn an arc intersecting previously drawn arc, at point N.
4. Draw the ray AX passing through N, then
5. Taking A ascentre and radius equal to 5 cm, draw an arc cutting AX at C.
6. Join BC.
7. The required triangle ABC is obtained.
8. Draw angle bisector of∠CAB and ∠ABC.
9. Mark their intersection as O.
10. With O as center, draw a circle with radius OD.

1. Hence, AY is the locus of points equidistant from AB and AC.
2. Hence, BZ is the locus of points equidistant from BA and BC.