arocks wrote: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

Please explain. Thanks.

the distance between any two points (x1,y1) and (x2,y2) on the coordinate plane = root( (x2-x1)^2+(y2-y1)^2) ..

Using the formula, the distance between the center (-2,-3) of the circle and the point outside the circle (4,-3) = root((4-((-2))^2+(-3-(-3))^2) = root (6^2) = 6 , now the radius of the circle will be less than 6 bcoz the point (4,-3) lies outside the circle..

Similarly the distance between (-2,-3) and the point inside the circle (-2,1) = root( (-2-(-2))^2+(1-(-3))^2) = root (4^2) = 4, the radius of the circle will be greater than 4 bcoz the point (-2,1) lies inside the circle ...

So the radius of the circle is a integer that lies between 4 and 6, which should be equal to 5 ... so the answer should be B ..

It's easy to solve this if you make a coordinate system and plot these points roughly.

If point (-2, 1) lies inside the circle, then the radius of the circle is more than 4 units. (From -3 to 1)
If point (4, -3) lies outside the circle, then the radius is less than 6 units (from -2 to 4).

Therefore the answer is 5 ie B.

Thanks. Got it!