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.
1) Steps of constructions:
- Draw a line segment BC = 6 cm.
- At B, draw a ray BX making an angle of 120o with BC.
- From the point, B cut an arc of radius 3.5 cm to meet ray BX at A.
- Join AC.
ABC is the required triangle.
Bisect BC and draw a circle with BC as diameter.
Draw perpendicular bisectors of AB. Let the two bisectors meet the ray of angle bisector of ∠ABC at point P. P is equidistant from AB and BC.
3) On measuring ∠BCP = 30°