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What is the length of the chord AB

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What is the length of the chord AB [#permalink] New post 29 Jan 2012, 22:52
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What is the length of the chord AB

(1) The center of the circle is at the Origin and the chord AB is parallel to y-axis with one end of it at (8,6)
(2) The equation of the circle is x^2 + y^2 = 100
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jan 2012, 02:14, edited 1 time in total.
Topic moved to DS subforum.
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Re: Co-ordinate Geometry DS - Please explain [#permalink] New post 29 Jan 2012, 23:32
Answer has to be A. It is parallel to y axis and we already know its length on top of the x-axis, i.e. 6. Now since the chord will mirror on the other side of x-axis, i.e when y is negative, we can double 6 to get the length of the chord, which will be 12 . We do not need the size of the circle and the size of the circle itself will not be sufficient. Hence the answer has to be A.
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Re: Co-ordinate Geometry DS - Please explain [#permalink] New post 29 Jan 2012, 23:48
A is sufficient

Statement A : It is given that the center of the circle is 0 (0,0) & 1 end point of the Chord AB A (8,6). Further AB is parallel to the Y - Axis. From the above we can form the triangle AOB with height of 6 & base of 8. Using Pytha theorem we can find the Hypoth OA which is the radius. From this it is possible to find the coordinates of B using Pythag theorem

Thus Sufficient

Statement B : From the eqn of circle we can only compute the radius of circle which is 10 & thus is insufficient

Hope this helps :-)
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Re: Co-ordinate Geometry DS - Please explain [#permalink] New post 29 Jan 2012, 23:52
boomtangboy wrote:
A is sufficient

Statement A : It is given that the center of the circle is 0 (0,0) & 1 end point of the Chord AB A (8,6). Further AB is parallel to the Y - Axis. From the above we can form the triangle AOB with height of 6 & base of 8. Using Pytha theorem we can find the Hypoth OA which is the radius. From this it is possible to find the coordinates of B using Pythag theorem

Thus Sufficient

Statement B : From the eqn of circle we can only compute the radius of circle which is 10 & thus is insufficient

Hope this helps :-)


Why do you need to use the pythagorean theorem. Its pretty simple as it is. 8,6 means one half is 6 units long since it is parallel to y axis. Just double (since the circle is centered at origin) 6*2=12 which is the length of the cord. Had it not been parallel to the y-axis, it was a whole different story altogether and pythagorean theorem could have come in.
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Re: Co-ordinate Geometry DS - Please explain [#permalink] New post 30 Jan 2012, 02:12
Expert's post
Topic moved to DS subforum.

kenguva wrote:
What is the length of the chord AB

(1) The center of the circle is at the Origin and the chord AB is parallel to y-axis with one end of it at (8,6)
(2) The equation of the circle is x^2 + y^2 = 100


What is the length of the chord AB

(1) The center of the circle is at the Origin and the chord AB is parallel to y-axis with one end of it at (8,6) --> as the circle is centered at the origin and chord AB is parallel to y-axis then the other end of the chord will be mirror reflection around x-axis:
Attachment:
1.PNG
1.PNG [ 12.79 KiB | Viewed 1430 times ]
So, the length of AB=12. Sufficient

(2) The equation of the circle is x^2 + y^2 = 100 --> just gives us an equation of a circle centered at the origin with radius equal to 10. No info about the chord. Not sufficient.

Answer: A.

For more on this topic check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

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Re: What is the length of the chord AB [#permalink] New post 14 Aug 2014, 04:43
equation of circle given.
one end of point given and given that chord is parallel to y axis => equation of chord given.
so can find other point
and hence the length of chord.
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Re: What is the length of the chord AB [#permalink] New post 14 Aug 2014, 04:43
equation of circle given.
one end of point given and given that chord is parallel to y axis => equation of chord given.
so can find other point
and hence the length of chord.
Re: What is the length of the chord AB   [#permalink] 14 Aug 2014, 04:43
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