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In the rectangular coordinate system are the points A and B equidistan

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In the rectangular coordinate system are the points A and B equidistan  [#permalink]

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New post 24 Nov 2018, 10:13
1
3
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

21% (01:58) correct 79% (01:44) wrong based on 47 sessions

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GMATbuster's Weekly Quant Quiz#10 Ques #8


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In the rectangular coordinate system are the points A and B equidistant from point C (1, 0)?
(l) Points A and B lie on circle R, which passes through origin and has a radius equal to 1.
(2) The length bisector of the line segment AB passes through point C.

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Re: In the rectangular coordinate system are the points A and B equidistan  [#permalink]

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New post 24 Nov 2018, 11:12
1
(1) If the circle has center at C (1,0) then A and B will be equidistant. If the circle say has center at (0,1) and passes through origin and A is (0,0) and B is (0,2) then A and B are NOT equidistant from C. Hence Insufficient.

(2) The question says length bisector, not perpendicular bisector. So, there can be many combinations of points A and B such that the mid point of AB has a line passing through C. Cannot say if the points are equidistant. Hence Insufficient.

Combined: In the case of the first circle with center C (1,0), the length bisector of AB will always pass through C. But, in case of the second circle with center (0,1) and A being (0,0) and B being (0,2), there will still be a line which passes through midpoint of AB and C, but A and B are not equidistant to C. Hence Insufficient.

Hence IMO, Option E
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Re: In the rectangular coordinate system are the points A and B equidistan  [#permalink]

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New post 24 Nov 2018, 11:12
B.
first statement is not sufficient as circle can have its diameter anywhere other than C(1,0) in that case A and B will have different length.

Stat 2 is sufficient as length bisector passes through C, and any point on length bisector will be eqidistance from A and B.

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Re: In the rectangular coordinate system are the points A and B equidistan   [#permalink] 24 Nov 2018, 11:12
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