6. A circle \(C\) in the complex plane has equation \(| z - 2 - 5 i | = a\). The point \(z _ { 1 }\) on \(C\) has the least argument of any point on \(C\), and \(\arg \left( z _ { 1 } \right) = \frac { \pi } { 4 }\).
Prove that \(a = \frac { 3 \sqrt { 2 } } { 2 }\).
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