New problem.

[Ozlemg]

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2.

[Frankenstein]

Hi,
Center of the circle is at(-2,-3).
(-2,1) is inside the circle. So distance between (-2,-3) and (-2,1) is less than r i.e 4<r
(4,-3) is outside the circle. So distance between (-2,-3) and (4,-3) is greater than r i.e 6>r
i.e. 4<r<6. So r=5.

Hence, B

[vikram4689]

Draw a rough figure.
Point that lies inside is at 4 unit distance & Point that lies outside is at 6 unit distance
Since radius is an integer only option left is 5. Hence r = 5.

[cans]

a(-2,-3); b(-2,1); c(4,-3)
ab=4 and ac=6.
b lies inside and c lies outside
thus 6>r>4
or r=5 (using the options )
IMO B