Question

Using ruler and compasses only:

1. Construct a triangle ABC with 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 drawn which is equidistant from A and C.

Answer 1

Steps of construction:

1. Draw a line segment BC = 6 cm.
2. At point B, construct an angle of 120° with BC.
3. On the ray forming the angle, mark point A such that AB = 3.5 cm.
4. Join AC. Thus, △ABC is constructed.
5. To draw the circle with BC as diameter, construct the perpendicular bisector of BC.
6. Let the perpendicular bisector meet BC at O. Then O is the midpoint of BC.
7. With centre O and radius OB or OC, draw a circle. This is the required circle with BC as diameter.
8. Now, to find a point P on the circle which is equidistant from A and C, construct XY, the perpendicular bisector of AC.
9. Let XY, the perpendicular bisector of AC meet the circle at point P.
10. Then PA = PC, because every point on the perpendicular bisector of AC is equidistant from A and C.