Question:
A line segment AB is of length 5 cm. Draw a circle of radius 4 cm passing through A and B. Can you draw a circle of radius 2 cm passing through A and B? Give reason in support of your answer.
Solution:
(1) Draw a line segment AB of 5cm.
(2) Draw the perpendicular bisectors of AB.
(3) With centre A and radius of 4cm, draw an arc which intersects the perpendicular bisector at point O. The point O will be the required centre.
(4) Join OA.
(5) With centre O and radius OA, draw a circle.
No, we cannot draw a circle of radius 2 cm passing through A and B because when we draw an arc of radius 2 cm with centre A, the arc will not intersect the perpendicular bisector and we will not find the centre.