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Find the area of the square that can be inscribed in a circle of radius $8\ cm$.
Given: An square inscribed in a circle of radius $8\ cm$.
To do: To find the area of the square.
Solution:
Let $ABCD$ be the square inscribed by the circle.
$\therefore$ radius $r=OA=OB=OC=OD=8\ cm$
$ABC$ is a right angled triangle, as $OA=8,\ OC=8$
$AC=8+8=16$
According to Pythagoras theorem,
Square of hypotenuse$=$Sum of squares of other two sides.
$\Rightarrow AC^2=AB^2+BC^2$
As $ABCD$ is a square all the sides are equal, $AB=BC$
$\Rightarrow AC^2=2AB^2$
$\Rightarrow 16^2=2AB^2$
$\therefore AB=8\sqrt{2}$
Therefore, side of the square $=8\sqrt{2}$
Area of square $=( 8\sqrt{2})^2=128\ cm^2$
Updated on: 10-Oct-2022
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