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Question
Using a ruler and compasses only:
- Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.
- 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.
- Measure ∠BCP.
Solution
Steps of construction:
- 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. - 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. - On mesuring, ∠BCP = 30°
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