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

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Senior Manager
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PS: Circle find the minor arc? (GMATPrep 1 ) [#permalink]

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New post 02 Aug 2008, 07:42
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Re: PS: Circle find the minor arc? (GMATPrep 1 ) [#permalink]

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New post 02 Aug 2008, 08:48
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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:

Kudos [?]: 327 [1], given: 0

Senior Manager
Senior Manager
User avatar
Joined: 19 Mar 2008
Posts: 352

Kudos [?]: 67 [0], given: 0

Re: PS: Circle find the minor arc? (GMATPrep 1 ) [#permalink]

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New post 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

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Re: PS: Circle find the minor arc? (GMATPrep 1 )   [#permalink] 02 Aug 2008, 09:01
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PS: Circle find the minor arc? (GMATPrep 1 )

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