The area of any cyclic quadrilateral ABCD is given by `A^(2) = (s -a) (s-b) (s-c) (s-d)`, where `2s = a + b ++ c + d, a, b, c and d` are the sides of the quadrilateral
Now consider a cyclic quadrilateral ABCD of area 1 sq. unit and answer the following question
When the perimeter is minimum, the quadrilateral is necessarily

Options

A. a square
B. a rectangle but not a square
C. a rhombus but not a square
D. none of these

Answer

A

Explanation

When the perimeter is minimum,
`s-a = s- b = s - c = s-d or a = b = c = d`
Therefore, ABCD is a square ( `:'` cyclic quadrilateral)