Center of the circle was (0,0)

We take a point (x,0) as one of the edge of rectangle

The edge just above (x,0) will have

y coordinate lying on the semicircle and given by

, hence its coordinate is

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Make sure you get the above part before you continue.

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Area of this rectangle will be given by

...............{2 times of x because the length will lie on both side of the axis}

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if you don't get the above thing try drawing the diagram.

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This area needs to be max. so try finding the maximum

value of Area(x)

for maxima

From above get the value of x for which A(x) is 0 . try this

value on A(x) to get max. area.

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Be sincere enough to read below after you have solved.

Spoiler:

Now find area(use +ve x).