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PQ and RS are 2 mutually perpendicular chords intersecting at X. QX =

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KarunMendiratta
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PQ and RS are 2 mutually perpendicular chords intersecting at X. QX = [#permalink] New post   07 Mar 2022, 00:23
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PQ and RS are 2 mutually perpendicular chords intersecting at X. QX = 3, PX = 5, XR = 2. What is the radius of circle O?

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\(\sqrt{23.56}\)
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Re: PQ and RS are 2 mutually perpendicular chords intersecting at X. QX = [#permalink] New post   13 May 2022, 04:49
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123444
Can you please tell me why the question is incomplete?
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Re: PQ and RS are 2 mutually perpendicular chords intersecting at X. QX = [#permalink] New post   13 May 2022, 21:32
Hello Sir,

This question doesn't mention where O is/doesn't indicate where these points are with respect to O's position. I could draw n no of circles and assume them to be O as the question stem fails to provide some association between O and the given line segments. Please let me know if i'm missing something.

Thanks.
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Re: PQ and RS are 2 mutually perpendicular chords intersecting at X. QX = [#permalink] New post   15 May 2022, 21:43
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123444 wrote:
Hello Sir,

This question doesn't mention where O is/doesn't indicate where these points are with respect to O's position. I could draw n no of circles and assume them to be O as the question stem fails to provide some association between O and the given line segments. Please let me know if i'm missing something.

Thanks.


A circle is denoted by its centre. So point O is the centre of this circle.
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PQ and RS are 2 mutually perpendicular chords intersecting at X. QX = [#permalink] New post   15 May 2022, 21:56
I understand the denotation sir however no information has been given in the question as to where this center lies(O) or if any of the points mentioned in the question are part of this circle. The intersection of those two chords is denoted by X so i'm not sure where to even start in this problem. Is there a simple diagram which can demystify this confusion?
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Re: PQ and RS are 2 mutually perpendicular chords intersecting at X. QX = [#permalink] New post   13 Jul 2022, 07:40
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To find SX= (PX * QX)/XR= 5 * 3 /2 = 7.5
To find the midpoint of chord PQ and RS,we have
Midpoint of PQ(M)=5+3=8/2=4
Midpoint of RS(N)=7.5+2=9.5/2=4.75
Now we have PM=QM=4 and SN=RN=4.75

OM=NX=RN-RX=4.75 - 2 =2.75
To find the radius which is OP=OQ
We use Pythagoras theorem,
OP=square root ( sqr(PM) +Sqr(OM))
=square root (4×4 + 7.75x7.75)
=square root(16+7.56)
Radius =square root(23.56)
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