Figure $10\mathrm{.}49$ shows a circle of radius $4$ units centered at A and a circle of radius $5$ units centered at B$.$ Points A and B are $7$ units apart.

a$.$ Describe points C and D in terms of their distances $($in units$)$ from points A and B$.$

b$.$ Describe the locations in Region $1$ in terms of their distances $($in units$)$ from points A and B$.$

c$.$ Describe the locations in Region $2$ in terms of their distances $($in units$)$ from points A and B$.$

d$.$ Describe the locations in Region $3$ in terms of their distances $($in units$)$ from points A and B$.$

e$.$ Are there any locations on the page that are more than $4$ units from A and more than $5$ units from B$?$ If so$,$ give some examples, if not, explain why not.