Question

Construct a triangle ABC such that AB = 7 cm, BC = 6 cm and CA = 5 cm. (use ruler and compass to do so).

(a) Draw the locus of the points such that

(i) it is equidistant from BC and BA.

(ii) it is equidistant from points A and B. 

(b) Mark P where the loci (i) and (ii) meet, measure and write length of PA.

Answer 1

We know that,

Locus of the points equidistant from two sides is the angle bisector between two sides.

Locus of the points equidistant from two points is the perpendicular bisector of the line joining two points.

Steps of construction:

1. Draw a line segment AB = 7 cm.

2. With A and B as center and radii 5 cm and 6 cm respectively draw arcs intersecting at C.

3. Join AC and BC.

4. Draw BD, angle bisector of B.

5. Draw XY perpendicular bisector of AB.

6. Mark point P, the intersection point of XY and BD.

7. Measure AP.

Hence, AP = 3.8 cm.