If `(m_i,1/m_i),i=1,2,3,4` are concyclic points then the value of `m_1m_2m_3m_4` is

Explanation

Given that `(m_(i),1//m),m_(i)gt0,i=1,2,3,4` are four distinct points on a circle.
Let the equation of circel be `x^(2)+y^(2)+2gx+2fy+c=0`
As the point `(m,1//m)` lies on it, we have
`m^(2)+(1)/(m^(2))+2gm+(2f)/(m)+c=0`
or `m^(4)+2gm^(3)+cm(2)+2fm+1=0`
Since `m_(1),m_(2),m_(3)` and `m_(4)` are the roots of this equation, the products of roots is 1,i.e.,
`m_(1),m_(2),m_(3),m_(4)=1`