11. The circle \(C\) has equation
$$x ^ { 2 } + y ^ { 2 } - 8 x - 10 y + 16 = 0$$
The centre of \(C\) is at the point \(T\).
- Find
- the coordinates of the point \(T\),
- the radius of the circle \(C\).
The point \(M\) has coordinates \(( 20,12 )\).
- Find the exact length of the line \(M T\).
Point \(P\) lies on the circle \(C\) such that the tangent at \(P\) passes through the point \(M\).
- Find the exact area of triangle \(M T P\), giving your answer as a simplified surd.