The complex number \(z\) satisfies \(|z-2-5\mathrm i|\le3\).
On an Argand diagram, sketch the region in which the point representing \(z\) can lie.[3]
Find exactly the maximum and minimum possible values of \(|z|\).[2]
It is given that \(0\le\arg z\le\frac14\pi\). With this extra information, find the maximum value of \(|z-6-\mathrm i|\). Label the point(s) that correspond to this maximum value on your diagram with the letter \(P\).[3]