A line segment $A B$ is of length $5 c m .$ Draw a circle of radius $4 c m$ passing through $A$ and $B .$ Can you draw a circle of radius $2 c m$ passing through $A$ and $B$ ? Give reason in support of your answer.

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Solution

Steps of Construction :

(i) Draw a line segment $A B = 5 c m .$

(ii) Draw a perpendicular besector of $A B .$

(iii) With center $A$ and radius $4 c m,$ draw an arc which intersects the perpendicular bisector at $O .$

(iv) With center $O$ and radius $O A$ draw a circle.
No, we cannot draw a circle of radius $2 c m$ passing through $A$ and $B$ because when we draw an arc of radius $2 c m$ with center $A$ , the arc will not intersect the perpendicular bisector and we will not find the center.

i.e., $2 + 2 = 4 c m$ is shorter than $5 c m .$

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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.

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