10. The circle \(C\) has centre \(A ( 2,1 )\) and passes through the point \(B ( 10,7 )\).
- Find an equation for \(C\).
The line \(l _ { 1 }\) is the tangent to \(C\) at the point \(B\).
- Find an equation for \(l _ { 1 }\).
The line \(l _ { 2 }\) is parallel to \(l _ { 1 }\) and passes through the mid-point of \(A B\).
Given that \(l _ { 2 }\) intersects \(C\) at the points \(P\) and \(Q\), - find the length of \(P Q\), giving your answer in its simplest surd form.
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