Question

Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.

1. Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
2. Construct the locus of points at a distance of 3.5 cm from A.
3. Construct the locus of points equidistant from AC and BC.
4. Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.

Answer 1

1. Steps of construction:
   1. Draw BC = 6.5 cm using a ruler.
   2. With B as center and radius equal to approximately half of BC, draw an arc that cuts the segment BC at Q.
   3. With Q as center and same radius, cut the previous arc at P.
   4. Join BP and extend it.
   5. With B as center and radius 5 cm, draw an arc that cuts the arm PB to obtain point A.
   6. Join AC to obtain ΔABC.
      
2. With A as center and radius 3.5 cm, draw a circle.
   The circumference of a circle is the required locus.
   
3. Draw CH, which is bisector of ΔACB. CH is the required locus.
   
4. Circle with center A and line CH meet at points X and Y as shown in the figure. xy = 5 cm (approximately).