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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

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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"Nowadays, people know the price of everything, and the value of nothing."Oscar Wilde

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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Giving +1 kudos is a better way of saying 'Thank You'.

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.
_________________

"Nowadays, people know the price of everything, and the value of nothing."Oscar Wilde

(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 [ 12.79 KiB | Viewed 2890 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.

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28 Jul 2014, 22:59

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Re: What is the length of the chord AB [#permalink]

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14 Aug 2014, 05:43

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]

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14 Aug 2014, 05:43

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]

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04 Jun 2016, 03:47

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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