7. The circle \(C\) has centre \(( 5,2 )\) and passes through the point \(( 7,3 )\).
- Find the length of the diameter of \(C\).
- Find an equation for \(C\).
- Show that the line \(y = 2 x - 3\) is a tangent to \(C\) and find the coordinates of the point of contact.