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# PS: Circle find the minor arc? (GMATPrep 1 )

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Senior Manager
Joined: 19 Mar 2008
Posts: 350
PS: Circle find the minor arc? (GMATPrep 1 ) [#permalink]

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02 Aug 2008, 07:42
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In the Circle above.doc [25 KiB]

Director
Joined: 10 Sep 2007
Posts: 922
Re: PS: Circle find the minor arc? (GMATPrep 1 ) [#permalink]

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02 Aug 2008, 08:48
1
KUDOS
Triangle OPR is a right angle triangle (Theorem that any triangle created on diameter of a circle is right angled triangle).
Angle POR = 180 - 35 - 90 = 55
Says centre of circle is X.
Triangle PXO is an isosceles triangle (two side radius of circle). So Angle XPO = 55
Angle XPR = 90 (Angle OPR) - 55 (XPO) = 35
Angle RPQ = 35 (Alternate Angles)
So Angle XPQ = 35 (angle RPQ) + 35 (angle XPR) = 70
Triangle XPQ is another isosceles triangle (two side radius of circle).
So PXQ = 180 - 70 - 70 = 40

I hope after this you can get the answer
Senior Manager
Joined: 19 Mar 2008
Posts: 350
Re: PS: Circle find the minor arc? (GMATPrep 1 ) [#permalink]

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02 Aug 2008, 09:01
abhijit_sen wrote:
Triangle OPR is a right angle triangle (Theorem that any triangle created on diameter of a circle is right angled triangle).
Angle POR = 180 - 35 - 90 = 55
Says centre of circle is X.
Triangle PXO is an isosceles triangle (two side radius of circle). So Angle XPO = 55
Angle XPR = 90 (Angle OPR) - 55 (XPO) = 35
Angle RPQ = 35 (Alternate Angles)
So Angle XPQ = 35 (angle RPQ) + 35 (angle XPR) = 70
Triangle XPQ is another isosceles triangle (two side radius of circle).
So PXQ = 180 - 70 - 70 = 40

I hope after this you can get the answer :wink:

Nice one. I got it. Thanks
+1 for you

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: PS: Circle find the minor arc? (GMATPrep 1 )   [#permalink] 02 Aug 2008, 09:01
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