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## GRE - Quantitative Reasoning - Coordinate geometry

### 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=

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

Since (-2, 1) lies inside the circle

r > distance between center (-2, -3) and point (-2, 1)

SInce (-2, -3) and (-2, 1) lie on a line parellel to y axis

distance between them = |-3-1| = 4

r > 4

We also know that (4 , -3) lies outside the circle

r < distance between center (-2, -3) and point (4 -3)

Since (-2, -3) and (4, -3) lie on a line parellel to x-axis

distance between them =  |-2-4| = 6

r<6

Since 4 < r < 6

and r is an integer

the only possible value of r is 5

B is correct