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 2a 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.