Algebra Level 5

$\large \begin{cases} {x^2 + y^2 =16 } \\ {z^2 + t^2 = 25} \\ { xt - yz = 20} \end{cases}$

If real numbers $$t , x , y , z$$ satisfy the system of equations above, find the maximum value of $$P = xz$$.

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