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Geometry: Dont take it for granted

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by thephoenix » Sun Oct 10, 2010 7:12 am
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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by shovan85 » Sun Oct 10, 2010 7:16 am
thephoenix wrote:it has been posted no.f times search u will get a link
thanks I got it but still worth a post ... as people can get involved in an active discussion :)
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by rohit_gmat » Sun Oct 10, 2010 7:46 am
shovan85 wrote:Explanations Please.
IMO A

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?
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by shovan85 » Sun Oct 10, 2010 8:23 am
rohit_gmat wrote:
shovan85 wrote:Explanations Please.
IMO A

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 ever :)
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by lokesh r » Sun Oct 10, 2010 11:55 pm
rohit_gmat wrote:
shovan85 wrote:Explanations Please.
IMO A

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 pi
Would be helpful if anycone can explain why is it multiplied by 2 in getting length of arc OP.
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by pharmxanthan » Mon Oct 11, 2010 12:10 am
Because the angle subtended by the chord at the center is double that at the circumference.
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by lokesh r » Mon Oct 11, 2010 3:39 am
pharmxanthan wrote:Because the angle subtended by the chord at the center is double that at the circumference.
Say in the figure attached we call center of the circle as A.

Do you mean angle PAO= 2 x angle PRO
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by fskilnik@GMATH » Mon Oct 11, 2010 7:22 am
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)
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by pharmxanthan » Mon Oct 11, 2010 4:06 pm
lokesh r wrote:
pharmxanthan wrote:Because the angle subtended by the chord at the center is double that at the circumference.
Say in the figure attached we call center of the circle as A.

Do you mean angle PAO= 2 x angle PRO
Yes.
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