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Is point P the center of the circle?

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Is point P the center of the circle?

by gmattesttaker2 » Sat Feb 15, 2014 5:24 pm
Hello,

For the following:

Point P is inside circle X. If A, B, and C are three different points on the
circumference of circle X, is point P the center of circle X?

(1) PA = PB
(2) PA = PC

I got this problem from a Geometry question set. The OA is given as E but I thought it should be D since only if P is the center of the circle will the above 2 conditions be met. Thanks for your help - Sri
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by Patrick_GMATFix » Sat Feb 15, 2014 9:42 pm
Hi again Sri,

The set of points equidistant from A and B form a line perpendicular to AB (also known as the perpendicular bisector of AB). For instance, when (1) states that PA=PB, P can be any point on the red line segment below. Likewise when (2) states that PA=PC, P can be any point on green the perpendicular bisector.
Image
I would have picked answer C since the center of the circle is the only point to satisfy both statements. I don't know why E would be correct.

-Patrick
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by gmattesttaker2 » Sun Feb 16, 2014 5:00 pm
Patrick_GMATFix wrote:Hi again Sri,

The set of points equidistant from A and B form a line perpendicular to AB (also known as the perpendicular bisector of AB). For instance, when (1) states that PA=PB, P can be any point on the red line segment below. Likewise when (2) states that PA=PC, P can be any point on green the perpendicular bisector.
Image
I would have picked answer C since the center of the circle is the only point to satisfy both statements. I don't know why E would be correct.

-Patrick
Hello Patrick,

Thank you very much for your excellent visual explanation. Thanks for all your help.

Best Regards,
Sri
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by gmattesttaker2 » Sun Feb 16, 2014 5:00 pm
Patrick_GMATFix wrote:Hi again Sri,

The set of points equidistant from A and B form a line perpendicular to AB (also known as the perpendicular bisector of AB). For instance, when (1) states that PA=PB, P can be any point on the red line segment below. Likewise when (2) states that PA=PC, P can be any point on green the perpendicular bisector.
Image
I would have picked answer C since the center of the circle is the only point to satisfy both statements. I don't know why E would be correct.

-Patrick
Hello Patrick,

Thank you very much for your excellent visual explanation. Thanks for all your help.

Best Regards,
Sri
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