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In the xy plane, the point (-2,-3) is the center of a circle

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In the xy plane, the point (-2,-3) is the center of a circle [#permalink] New post 02 May 2012, 17:55
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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 how to approach such questions.
Bunuel: Kindly post a link of similar questions for practice.
Thanks in advance.
[Reveal] Spoiler: OA
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Re: circle [#permalink] New post 02 May 2012, 20:13
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(-2,-3) is the center of the circle.

(-2,1) lies inside the circle => The radius of the circle is greater than 4 units (as the x coordinates of the center and the point are the same, the distance from the center to the point is the difference in y coordinates, or 4 units)

(4,-3) lies outside the circle => The radius of the circle is less than 6 units

Between 4 and 6, the only integer is 5. Therefore the radius of the circle must be 5 units.

Option (B)
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Re: In the xy plane, the point (-2,-3) is the center of a circle [#permalink] New post 02 May 2012, 23:21
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saishankari 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 how to approach such questions.
Bunuel: Kindly post a link of similar questions for practice.
Thanks in advance.


I'd quickly mark the points on a plane to SEE the whole picture:
Attachment:
Circle.png
Circle.png [ 11.45 KiB | Viewed 2489 times ]
You can see that the radius must be more than 4 (since the distance between (-2, -3) and (-2, 1) is 4) but less than 6 (since the distance between (-2,-3) and (4, -3) is 6). It's given that r is an integer therefore r=5.

Answer: B.

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.
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Re: In the xy plane, the point (-2,-3) is the center of a circle   [#permalink] 02 May 2012, 23:21
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In the xy plane, the point (-2,-3) is the center of a circle

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