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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Is point P the center of the circle?
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gmattesttaker2
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Patrick_GMATFix
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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.
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
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.
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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gmattesttaker2
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Hello Patrick,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.
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
Thank you very much for your excellent visual explanation. Thanks for all your help.
Best Regards,
Sri
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gmattesttaker2
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Hello Patrick,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.
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
Thank you very much for your excellent visual explanation. Thanks for all your help.
Best Regards,
Sri
