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\includegraphics[max width=\textwidth, alt={}, center]{e69332d0-2e45-4a86-a1f9-5d83bca1ad9b-4_885_967_255_589} The diagram shows the curve \(y = ( 6 x + 2 ) ^ { \frac { 1 } { 3 } }\) and the point \(A ( 1,2 )\) which lies on the curve. The tangent to the curve at \(A\) cuts the \(y\)-axis at \(B\) and the normal to the curve at \(A\) cuts the \(x\)-axis at \(C\).

1. Find the equation of the tangent \(A B\) and the equation of the normal \(A C\).
2. Find the distance \(B C\).
3. Find the coordinates of the point of intersection, \(E\), of \(O A\) and \(B C\), and determine whether \(E\) is the mid-point of \(O A\).