Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

Let a
rectangle of length *l* and breadth *b* be inscribed in the
given circle of radius *a*.

Then, the
diagonal passes through the centre and is of length 2*a* cm.

Now, by applying the Pythagoras theorem, we have:

∴Area of the rectangle,

By the second derivative test, when, then the area of the rectangle is the maximum.

Since, the rectangle is a square.

Hence, it has been proved that of all the rectangles inscribed in the given fixed circle, the square has the maximum area.

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