Question

Using a ruler and compasses only: 

(i) Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°

(ii) 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. 

(iii) Measure ∠BCP.

Answer 1

Steps of Construction:

(i) Draw a line BC = 6 cm. 

With the help of the point B, draw ∠ABC = 120°. 

(ii) Taking radius 3.5 cm cut BA = 3.5 cm. 

Join A to C. 

Draw ⊥ bisector MN of BC. 

(iii) Draw a circle 0 as centre and OC as radius. 

Draw angle bisector of ∠ABC which intersects circle at P. 

Join BP and CP. 

Now, ∠BCP = 30°.