Question

Using a ruler and compasses only: 

1. Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.
2. In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC. 
3. Measure ∠BCP.

Answer 1

Steps of construction: 

1. Draw a line segment BC = 6 cm.
   At B, draw a ray BX making an angle of 120° with BC. with B as center and radius 3.5 cm, out off AB = 3.5 cm. Join AC
   Thus, ABC is the required triangle. 
2. Draw perpendicular bisector MN of BC at point O. With O as center and radius = OB, draw a cirde.
   Draw angle bisector of ∠ABC which meets the circle at point P.
   Thus, point P is equidistant from AB and BC. 
3. On mesuring, ∠BCP = 30°