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26 Oct 2021, 01:30
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
29% (01:58) correct
71%
(02:18)
wrong
based on 63
sessions
History
Date
Time
Result
Not Attempted Yet
In the coordinate system, the center of a circle lies at (2, 3). If point A with coordinates (-1, 7) does not lie outside the circle, which of the following points must lie inside the circle?
I. (0, 7)
II. (5, -1)
III. (-2, 7)
A. I only
B. II only
C. III only
D. I and II only
E. None of the above
I. (0, 7)
II. (5, -1)
III. (-2, 7)
A. I only
B. II only
C. III only
D. I and II only
E. None of the above
26 Oct 2021, 01:54
Kudos
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Bunuel
Solution:
We are given that point \((-1,7)\) does not lie outside the circle. This means that the point \((-1,7)\) either:
1. Lie on the circle. In this case, the radius is the distance between \((2,3)\) and \((-1,7)\)
2. Lie inside the circle. In this case, the radius is more than the distance between \((2,3)\) and \((-1,7)\)
Distance between \((2,3)\) and \((-1,7)\) \(= \sqrt{(-1-2)^2+(7-3)^2}=5\)
Thus, the radius of the circle \(r ≤ 5\).
I. \((0, 7)\)
Distance between \((2,3)\) and \((0,7)\) \(= \sqrt{(0-2)^2+(7-3)^2}=\sqrt{20}\). This is definitely less than 5.
Thus \((0, 7)\) lie inside the circle. We can be sure of it.
II. \((5,-1)\)
Distance between \((2,3)\) and \((5,-1)\) \(= \sqrt{(5-2)^2+(-1-3)^2}=\sqrt{25}\). This is equal to 5.
Thus \((5,-1)\) does not lie inside the circle. In fact, it lies on the circle.
II. \((-2,7)\)
Distance between \((2,3)\) and \((-2,7)\) \(= \sqrt{(-2-2)^2+(7-3)^2}=\sqrt{32}\). This is greater than 5.
Thus \((-2,7)\) does not lie inside the circle.
Hence the right answer is Option A.
29 Jan 2025, 08:46
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