Math Help - Complex Number question

1. Complex Number question

Hi everyone, anyone fancy helping out on yet another question

A complex number $z$ is represented by the point P on an Argand diangram, $|z-5-12i| = 3$.

a. Sketch the locus of P.

This I could do, circle, centre (5, 12), radius of 3.

b. Find the maximum and minimum values for $|z|$.

For this I found the distance of the centre of the circle from the origin, and then $\pm$ the radius to get 10 and 16, is this correct?

c. Find the min and max values for $arg{z}$ in radians to 2dp.

Argument is $tan^{-1}{\frac{12}{5}}$, but not sure where to go to get the max and min values from here?