Question

Using ruler and compass only:

1. Construct a triangle ABC with BC = 6 cm, ∠ABC = 120° and AB = 3.5 cm. 
2. In the above figure, 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

• Draw a line segment BC = 6 cm.
• At point B, construct a ray BX that makes an angle of 120° with BC. Taking B as the centre and a radius of 3.5 cm, mark point A on this ray so that AB = 3.5 cm.
• Join A to C to obtain triangle ABC.
• Construct the perpendicular bisector of BC, meeting BC at O. With O as the centre and radius OB, draw a circle having BC as its diameter.
• Bisect angle ABC. The angle bisector will intersect the circle at point P. Therefore, point P is equidistant from AB and BC.
• Finally, measure ∠BCP.

Hence, ∠BCP = 30°.