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In the x-y plane, there are circle C and line K. If the radius of the

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In the x-y plane, there are circle C and line K. If the radius of the  [#permalink]

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New post 29 Mar 2016, 23:22
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In the x-y plane, there are circle C and line K. If the radius of the circle is 3 and the center of the circle is (0,0), does the line K intersect with the circle?

1) The line K passes through (2,2)
2) The line K passes through (4,4)


* A solution will be posted in two days.

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Re: In the x-y plane, there are circle C and line K. If the radius of the  [#permalink]

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New post 30 Mar 2016, 00:40
1
Radius of the circle = 3 --> Max distance of circle from origin to any point on the circumference = 3

St1: Distance of line K from origin = sqrt(4 + 4) = 2*sqrt(2) < 3 --> Line K passes through the circle. Sufficient

St2: Distance of line K from origin = sqrt(16 + 16) = 4*sqrt(2) > 3 --> Line K may or may not pass through the circle. Not Sufficient.

Answer: A
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Re: In the x-y plane, there are circle C and line K. If the radius of the  [#permalink]

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New post 03 Apr 2016, 01:40
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In the x-y plane, there are circle C and line K. If the radius of the circle is 3 and the center of the circle is (0,0), does the line K intersect with the circle?

1) The line K passes through (2,2)
2) The line K passes through (4,4)


In the original condition, there is already a circle and the question is if the line passes through the circle.
For 1), (2,2) is already in the circle, which is always yes and sufficient.
For 2), if the line passes through (4,4), it might meet the circle or not, which is not sufficient.
Thus, the answer is A.
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Re: In the x-y plane, there are circle C and line K. If the radius of the  [#permalink]

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New post 17 Apr 2016, 13:02
if radius of the circle is 3 units,then any point whose distance from the origin is less than 3 units lies inside the circle.
Statement A clearly fulfills this condition as any point on a line which lies inside the circle will intersect the circle surely.
Statement B says that the line k may or may not intersect the circle.
so clearly correct answer option A
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Re: In the x-y plane, there are circle C and line K. If the radius of the  [#permalink]

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New post 18 Oct 2016, 07:03
1
MathRevolution wrote:
In the x-y plane, there are circle C and line K. If the radius of the circle is 3 and the center of the circle is (0,0), does the line K intersect with the circle?

1) The line K passes through (2,2)
2) The line K passes through (4,4)


* A solution will be posted in two days.


Responding to a pm:

Quote:
As per this St2 is not suff , however we know that the line( 4,4) is passing outside the circle , so how can we say that it may or may not intersect circle.
I thought it will not intersect circle.


(4, 4) is only one point through which the line passes. To define a line uniquely, you need two of its points.
What if I tell you that the line passes through (4, 4) and (0, 0). In this case, will it intersect the circle? Yes.
On the other hand, if I tell you that the line passes through (4, 4) and (4, 0). In this case, will it intersect the circle? No.
So according to statement 2, the line may or may not intersect the circle.
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Re: In the x-y plane, there are circle C and line K. If the radius of the  [#permalink]

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New post 19 Oct 2016, 00:17
VeritasPrepKarishma wrote:
MathRevolution wrote:
In the x-y plane, there are circle C and line K. If the radius of the circle is 3 and the center of the circle is (0,0), does the line K intersect with the circle?

1) The line K passes through (2,2)
2) The line K passes through (4,4)


* A solution will be posted in two days.


Responding to a pm:

Quote:
As per this St2 is not suff , however we know that the line( 4,4) is passing outside the circle , so how can we say that it may or may not intersect circle.
I thought it will not intersect circle.


(4, 4) is only one point through which the line passes. To define a line uniquely, you need two of its points.
What if I tell you that the line passes through (4, 4) and (0, 0). In this case, will it intersect the circle? Yes.
On the other hand, if I tell you that the line passes through (4, 4) and (4, 0). In this case, will it intersect the circle? No.
So according to statement 2, the line may or may not intersect the circle.


Thanks Karishma, I made a silly mistake... In my mind I imagined that both points are at (4,4).
Thanks again for your help.
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Re: In the x-y plane, there are circle C and line K. If the radius of the  [#permalink]

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New post 10 Oct 2017, 20:22
VeritasPrepKarishma Bunuel.

Hows A sufficient ? What if line goes from (-2,-2) to (2,2) and stays within the circle.
or am i visually imagining a circle with circumference thats more of a square than a cirlce ?
Thanks
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Re: In the x-y plane, there are circle C and line K. If the radius of the  [#permalink]

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New post 10 Oct 2017, 21:48
mbsingh wrote:
VeritasPrepKarishma Bunuel.

Hows A sufficient ? What if line goes from (-2,-2) to (2,2) and stays within the circle.
or am i visually imagining a circle with circumference thats more of a square than a cirlce ?
Thanks

Line has not starting or ending point. You cant assume it to start at (-2,-2) and end at (2,2) hence the line which will pass through (2,2) will intersect the circle. Hence A

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Re: In the x-y plane, there are circle C and line K. If the radius of the  [#permalink]

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New post 11 Oct 2017, 03:29
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mbsingh wrote:
VeritasPrepKarishma Bunuel.

Hows A sufficient ? What if line goes from (-2,-2) to (2,2) and stays within the circle.
or am i visually imagining a circle with circumference thats more of a square than a cirlce ?
Thanks


You are thinking about a "line segment" (which has end points).
A "line" extends infinitely in both directions (even though we are not able to show it on paper). So it cannot stay within the circle.
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Re: In the x-y plane, there are circle C and line K. If the radius of the &nbs [#permalink] 11 Oct 2017, 03:29
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