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)
1) Draw a line segment BC = 6 cm.
2) Draw ∠ ABC = 120°.
3) With centre B and radius BA = 3.5 cm, draw an arc.
4) Join AB and AC.

(ii) 
1) Draw the right bisector on line BC cut the BC line at M.
2) Draw another bisector of line AC.
3) With M as centre and radius MB draw a circle cut AC bisector at P.

(iii) ∠ BCP = 30°