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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.
Given:
A line segment $AB$ is of length $5\ cm$.
To do:
We have to draw a circle of radius $4\ cm$ passing through $A$ and $B$ and if possible a circle of radius $2\ cm$ passing through $A$ and $B$.
Solution:
Steps of construction:
1. Draw a line segment $AB = 5\ cm$.
2. Draw a perpendicular bisector of $AB$.
3. With centre $A$ and radius $4\ cm$, draw an arc which intersects the perpendicular bisector at $O$.
4. With centre $O$ and radius $4\ cm$, draw a circle which passes through $A$ and $B$.
With radius $2\ cm$, we cannot draw the circle passing through $A$ and $B$ as the diameter ($2 + 2 = 4\ cm$) is shorter than $5\ cm$.
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