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Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?
To do:
We have to draw a circle and any two of its diameters and find the figure obtained
(a) By joining the ends of the diameters.
(b) If the diameters are perpendicular to each other.
Solution:
Draw a circle with the centre '$O$'.
Let $AB$ and $CD$ be two diameters of the above circle.
(a) Join the ends of the diameters.
We get the quadrilateral $ABCD$.
We know that,
The diameters of a circle are equal in length.
This implies,
The diagonals of the quadrilateral $ABCD$ are equal in length.
The radii of a circle are equal in length.
$\Rightarrow OA=OB=OC=OD=$ radius.
If a quadrilateral has diagonals of equal length bisecting each other, then it is a rectangle.
Therefore, $ABCD$ is a rectangle.
(b) The diameters $AB$ and $CD$ of the circle are perpendicular to each other.
Join the ends of the diameters.
We get the quadrilateral $ABCD$.
We know that,
The diameters of a circle are equal in length.
This implies,
The diagonals of the quadrilateral $ABCD$ are equal in length.
We know that,
The radii of a circle are equal in length.
$\Rightarrow OA=OB=OC=OD=$ radius.
If a quadrilateral has diagonals of equal length and bisecting each other perpendicularly, then it is a square.
Therefore, $ABCD$ is a square.
To check the answers we have to measure the lengths of the figures obtained.
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