Question

Use ruler and compasses only for this question.

1. Construct ΔABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60°.
2. Construct the locus of points inside the triangle which are equidistant from BA and BC.
3. Construct the locus of points inside the triangle which are equidistant from B and C.
4. Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.

Answer 1

Steps of construction:

1. Draw line BC = 6 cm and an angle CBX = 60°. Cut off AB = 3.5. Join AC, triangle ABC is the required triangle.
2. Draw perpendicular bisector of BC and bisector of angle B.
3. Bisector of angle B meets bisector of BC at P.
   `=>` BP is the required length, where, PB = 3.5 cm
4. P is the point which is equidistant from BA and BC, also equidistant from B and C. 

 
PB = 3.6 cm