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O is the center of the circle and OS=SQ.
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15 Jul 2021, 05:59
Expert Reply
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Question Stats:
42% (01:02) correct
57% (01:34) wrong based on 14 sessions
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GRE O is the center of the circle and OS=SQ..jpg [ 10.26 KiB | Viewed 1344 times ]
O is the center of the circle and OS=SQ.
Quantity A
Quantity B
PQ
OR
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
O is the center of the circle and OS=SQ.
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15 Jul 2021, 08:15
1
Let's Join O and P as shown in the image below
Attachment:
image.jpg [ 9.84 KiB | Viewed 1298 times ]
In \(\triangle\)POR -> OP = OR = Radius => \(\triangle\)POR is an isosceles triangle.
\(\angle\)OSP = \(90^{\circ}\) [ As \(\angle\)PSQ= \(90^{\circ}\) ] And we know that, in an Isosceles Triangle the perpendicular drawn from the vertex tot he non equal side, bisects the side
=> OS will bisect PR => PS = SR
Now, consider \(\triangle\)PSQ and \(\triangle\)RSO PS = SR (proved above) OS = OQ (given) And the included angle, \(\angle\)PSQ = \(\angle\)RSO = \(90^{\circ}\) => \(\triangle\)PSQ ≅ \(\triangle\)RSO [Congruent triangles, all corresponding sides and all corresponding angles will be equal] => PQ = OR => Quantity A = Quantity B
So, answer will C Hope it helps!
Watch the following video to Learn Basics of Circles
gmatclubot
O is the center of the circle and OS=SQ. [#permalink]