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A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding major segment.
Given:
A chord of a circle of radius $10\ cm$ subtends a right angle at the center.
To do:
We have to find the area of the corresponding major sector.
Solution:
As the radius of the circle$=OA=OB=10\ cm$
Angle subtended by the chord $=\angle AOB=\theta=90^{\circ}$
Area of the major sector$=$ Area of the circle$-$Area of the minor sector
$=\pi r^2-\frac{\pi\theta}{360^{\circ}}\times OA\times OB$
$=3.14\times10\times10-3.14\times\frac{90^{\circ}}{360^{\circ}}\times10\times10$
$=314-78.5$
$=235.5\ cm^2$
Therefore, the area of the major sector is $235.5\ cm^2$.
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