What makes four points concyclic?

Geometry Level 2

If (mi,1mi)\left(m_i,\dfrac{1}{m_i}\right) where i=1,2,3,4i=1,2,3,4 are the coordinates of four concyclic points, then what is the value of m1m2m3m4m_1m_2m_3m_4?

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