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

Question

In the rectangular coordinate system are the points A and B equidistant from point C (1, 0)?

(1) Points A and B lie on circle R, which passes through origin and has a radius equal to 1.
(2) The bisector of the line segment AB passes through point C

Bunuel · Answer

Check the diagram: https://gmatclub.com/forum/download/file.php?id=35395 In both cases (orange line and green line), A and B are endpoints of diameters (origin cuts AB in half). Bisector - x-axis. Answer: E. Untitled.png

mohitkhanna.31 · Answer

Hi Bunnel,

Can you please elaborate this answer?

I am not able to connect how you reached the same.

Thanks,

Bunuel · Answer

Not sure what to elaborate... The image above gives two positions of A and B (green and orange) both of them satisfy the statements but give different answer to the question whether A and B equidistant from point C (1, 0).

mrinal0308 · Answer

statement 1: Insufficient
we know that the circle passes through the origin and has a radius of 1, and A and B are points located on the circle. It says nothing about C. C (1,0) can be the origin and so, A and B can be equidistant from C OR it is also possible that (-1, 0) is the origin and so, A and B's distance from C cant be calculated.

Statement 2: Insufficient: 
It says nothing about the position of A and B. C can be or cannot be equidistant from a and b.

Combining both, we do not get any conclusion still as we aren't sure of the origin and radius of the circle.

E should be the answer.

parnamsiddharth · Answer

The locus of a point equidistant from 2 points is perpindicular bisector... as c passes through perpendicular bisector... its equidistant from a and b.

Sent from my iPhone using GMAT Club Forum

ashygoyal · Answer

Answer is B.
 
First of all the diagram that all of you are looking at, is wrong. Since it is mentioned in first statement that circle passes through origin i.e. (0,0) should lie on circumference of circle. But in the diagram mentioned by Bunuel, its not the case.

Coming to answer, statement 1 doesnt tell us any info about points A and B. They can be anywhere on circle. Hence A is insufficient.

For Statement 2, the logic/ reason quoted by @parnamsiddharth is correct. If point C lies on bisector of line segment AB, C would always be equidistant from A & B. Hence second statement is sufficient.

Thus the answer must be B.

Thanks,
ashygoyal

akshata19 · Answer

Answer should be E 
Stmnt 1 - insufficient as explained above 
Stmnt 2 - it mentions bisector not perpendicular bisector 
A bisector simply means it cuts it into equal half
Hence we cannot conclude it is equidistant

Regards,
Akshata

Sent from my HTC One E9s dual sim using  GMAT Club Forum mobile app

ashygoyal · Answer

I think, i missed this point (as stated by akshata19). There is a difference between a perpendicular bisector and a plain 'bisector'.

In that case, E should be the answer.

Thanks and Regards, 
ashygoyal

Bunuel · Answer

A  perpendicular bisector  is a line which cuts a line segment into two equal parts  at 90° .

A line segment  bisector  is a line which cuts a line segment into two equal parts.

praneet87 · Answer

Can we assume that the origin is on the circle? just like points A & B? even though it doesnt change the answer?

adityapareshshah · Answer

Bunuel ,

It's mentioned in the question that the circle passes through the origin. However in the diagram, it is shown that the origin is the center of the circle. Is this correct interpretation ? Am I missing anything?

Though the answer will still be E as we aren't sure about the quadrants through which the circle passes through. Option A would have been sufficient, if is question stem specified that the center of the circle lies on the X-axis.

Bunuel · Answer

This changes nothing: https://gmatclub.com/forum/download/file.php?id=35548 The answer is still E. P.S. The red part is also not true. Check the image. Circle.png

bumpbot · Answer

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

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