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
The minimum value of the sum of the lenghts of diagonals is

Options

A. `2sqrt2`
B. 2
C. `sqrt2`
D. none of these

Answer

A

Explanation

If the length of diagonals and `d_(1) and d_(2)`, then the area of quadrilateral is given by
Area `=(1)/(2) d_(1) d_(2) sin theta`, where `theta` is angle between diagonals
`d_(1) d_(2) = (2)/(sin theta) or d_(1) d_(2) ge 2`
Also, `d_(1) + d_(2) ge 2 sqrt(d_(1) d_(2)) ge 2 sqrt2`