Mathematics
A line segment AB is of length 8 cm. Draw a circle of radius 5 cm that passes through A and B.
Can you draw a circle of radius 3 cm passing through A and B ? Give reason in support of your answer.
Circles
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Answer
Steps of construction:
Draw a line segment AB = 8 cm.
Draw the perpendicular bisector of AB.
Mark the intersection point of the perpendicular bisector and the line passing through midpoint of AB as O (the required center).
With center O and radius OA = 5 cm, draw a circle.
The circle will pass through both A and B.
No, a circle of radius 3 cm cannot pass through A and B.
The maximum possible radius of a circle passing through A and B is half of AB, i.e., 4 cm (when the center is at the perpendicular bisector). If the radius is 3 cm, the total diameter of such a circle would be 6 cm, which is less than AB = 8 cm. Thus, it is not possible to draw a circle of radius 3 cm passing through A and B.
Hence, a circle of radius 3 cm cannot pass through A and B.
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