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A circle centered at (4,-1) intersects the x-axis and y-axis at 2

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Director
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Joined: 18 Feb 2019
Posts: 581
Location: India
GMAT 1: 460 Q42 V13
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A circle centered at (4,-1) intersects the x-axis and y-axis at 2  [#permalink]

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New post 09 Mar 2019, 09:27
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A circle centered at (4,-1) intersects the x-axis and y-axis at 2 points each. Three points out of the four intercept points are taken to form a triangle. If two vertices of the triangle are (0,-8) and (12,0), which of the following could be the third vertex?

I. (-4,0)
II. (0,-6)
III. (0,6)

A. I only
B. II only
C. III only
D. I&III only
E. I,II & III
Manager
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Joined: 12 Apr 2011
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Concentration: Strategy, Marketing
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Re: A circle centered at (4,-1) intersects the x-axis and y-axis at 2  [#permalink]

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New post 09 Mar 2019, 12:30
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1
kiran120680 wrote:
A circle centered at (4,-1) intersects the x-axis and y-axis at 2 points each. Three points out of the four intercept points are taken to form a triangle. If two vertices of the triangle are (0,-8) and (12,0), which of the following could be the third vertex?

I. (-4,0)
II. (0,-6)
III. (0,6)

A. I only
B. II only
C. III only
D. I&III only
E. I,II & III


Two points intersecting the x-axis will be equidistant from the centre.
Hence is one of the points is (12,0), it is 8 units to the right of the centre (4,-1) along the x-axis. The other point will be 8 units to the left of the centre and will lie at (-4,0)

Two points intersecting the y-axis will be equidistant from the centre.
Hence is one of the points is (0,-8), it is 7 units below the centre of (4,-1) along the y-axis. The other point will be 7 units above the centre and will lie at (0,6)

Hence D is the correct answer.
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Re: A circle centered at (4,-1) intersects the x-axis and y-axis at 2  [#permalink]

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New post 28 Aug 2019, 11:31
kiran120680 wrote:
A circle centered at (4,-1) intersects the x-axis and y-axis at 2 points each. Three points out of the four intercept points are taken to form a triangle. If two vertices of the triangle are (0,-8) and (12,0), which of the following could be the third vertex?

I. (-4,0)
II. (0,-6)
III. (0,6)

A. I only
B. II only
C. III only
D. I&III only
E. I,II & III


Anybody can try explaining this one?
I drew the figure and took a calculated guess of option D and which turns out to be correct but that is not what I want to do.

Thank you!
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Re: A circle centered at (4,-1) intersects the x-axis and y-axis at 2   [#permalink] 28 Aug 2019, 11:31
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