Problem Solving

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

Can some help me with the above question?

Hi,
Center of the circle is (-2,-3).
(-2,1) is inside the circle. So, distance of this point from center is less than radius.
Distance between (-2,-3) and (-2,1) is 4 units.
So, r > 4
(4, -3) lies outside the circle. So, distance of this point from center is more than radius.
Distance between (-2,-3) and (4,-3) is 6 units.
So, r < 6
So, 4<r<6. r is an integer.
So, r=5

Hence, B

4<R<6

Thus R is 5

distance between (-2,-3) and (-2,1) is 1-(-3) = 4
distance between (-2,-3) and (4,-3) is 4-(-2) = 6

thus 4< r < 6
5 it is.