Write True or False and justify your answer in each of the following:
$A$ circle of radius $3 \, cm$ can be drawn through two points $A$ and $B$ such that $AB = 6 \, cm$.
$A$ circle of radius $3 \, cm$ can be drawn through two points $A$ and $B$ such that $AB = 6 \, cm$.
(A) The radius of the circle is $r = 3 \, cm$.
The diameter of the circle is $d = 2 \times r = 2 \times 3 \, cm = 6 \, cm$.
Since the distance between the two points $A$ and $B$ is $AB = 6 \, cm$,which is equal to the diameter of the circle,a circle can indeed be drawn passing through these two points with $AB$ as its diameter.
Therefore,the given statement is True.
The diameter of the circle is $d = 2 \times r = 2 \times 3 \, cm = 6 \, cm$.
Since the distance between the two points $A$ and $B$ is $AB = 6 \, cm$,which is equal to the diameter of the circle,a circle can indeed be drawn passing through these two points with $AB$ as its diameter.
Therefore,the given statement is True.
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