A circle has radius $12\ cm$. What is the length of the longest stick that can be placed inside this circle such that the two ends of the stick lie on the circle? Choose the correct option.
$( a).\ 12\ cm$
$( b).\ 24\ cm$
$( c).\ 18\ cm$
$( d).\ 36\ cm$

Given: A circle has radius $12\ cm$.

To do: To find the length of the longest stick that can be placed inside this circle such that the two ends of the stick lie on the circle.

Solution:

As given, radius of the circle $r=12\ cm$

Length of the longest stick that can be placed inside this circle such that the two ends of the stick lie on the circle is the length of the longest chord of the circle.

The longest chord of the circle is the diameter

$\therefore$ Diameter, $D=r\times2$

$\Rightarrow D=12\times2$

$=24\ cm$

Thus, option $( b)$ is correct.

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Updated on: 10-Oct-2022

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