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The diagram shows the circle with equation \(x ^ { 2 } + y ^ { 2 } - 8 x - 6 y - 20 = 0\).
- Find the centre and radius of the circle.
The circle crosses the positive \(x\)-axis at the point \(A\).
- Find the equation of the tangent to the circle at \(A\).
- A second tangent to the circle is parallel to the tangent at \(A\). Find the equation of this second tangent.
- Another circle has centre at the origin \(O\) and radius \(r\). This circle lies wholly inside the first circle. Find the set of possible values of \(r\).