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Geometry: Dont take it for granted
Source: Beat The GMAT — Problem Solving |
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thephoenix
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it has been posted no.f times search u will get a link
Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working
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rohit_gmat
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IMO Ashovan85 wrote:Explanations Please.
r = 18/2 = 9
total upper half = 1/2 x 2 x pi x r = 9 pi
Arc OP = 2 x (35/360) x 2 x pi x 9 = 7/2 pi
And its opposite arc shud be the same since the lines are parallel, so we have :
9 pi - 2(7/2 pi) = 2 pi
Is that correct?
Great... the most concise answer everrohit_gmat wrote:IMO Ashovan85 wrote:Explanations Please.
r = 18/2 = 9
total upper half = 1/2 x 2 x pi x r = 9 pi
Arc OP = 2 x (35/360) x 2 x pi x 9 = 7/2 pi
And its opposite arc shud be the same since the lines are parallel, so we have :
9 pi - 2(7/2 pi) = 2 pi
Is that correct?
Arc OP = 2 x (35/360) x 2 x pi x 9 = 7/2 pirohit_gmat wrote:IMO Ashovan85 wrote:Explanations Please.
r = 18/2 = 9
total upper half = 1/2 x 2 x pi x r = 9 pi
Arc OP = 2 x (35/360) x 2 x pi x 9 = 7/2 pi
And its opposite arc shud be the same since the lines are parallel, so we have :
9 pi - 2(7/2 pi) = 2 pi
Is that correct?
Would be helpful if anycone can explain why is it multiplied by 2 in getting length of arc OP.
Say in the figure attached we call center of the circle as A.pharmxanthan wrote:Because the angle subtended by the chord at the center is double that at the circumference.
Do you mean angle PAO= 2 x angle PRO
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fskilnik@GMATH
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Another approach:
01. Angle ORP (35 degrees) is inscribed, therefore (minor) arc OP measures 70 degrees.
02. Angle RPQ measures 35 degrees (parallelism), therefore (minor) arc QR measures 70 degrees.
03. From the fact that arc OPQR measures 180 degrees, (minor) arc PQ measures 40 degrees.
Finally, (minor) arc PQ measures 40/360 = 1/9 of 2*pi*(r=9) , then answer is surely 2pi (choice A)
01. Angle ORP (35 degrees) is inscribed, therefore (minor) arc OP measures 70 degrees.
02. Angle RPQ measures 35 degrees (parallelism), therefore (minor) arc QR measures 70 degrees.
03. From the fact that arc OPQR measures 180 degrees, (minor) arc PQ measures 40 degrees.
Finally, (minor) arc PQ measures 40/360 = 1/9 of 2*pi*(r=9) , then answer is surely 2pi (choice A)
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Yes.lokesh r wrote:Say in the figure attached we call center of the circle as A.pharmxanthan wrote:Because the angle subtended by the chord at the center is double that at the circumference.
Do you mean angle PAO= 2 x angle PRO
