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length Minor Arc

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Saj
 Post subject: length Minor Arc
 Post Posted: Sat Jul 05, 2008 7:17 am 
Image
guys,

could you pls help me on th question attached
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Maverick
 Post subject:
 Post Posted: Sun Jul 13, 2008 2:21 am 
Imagine the Center C on the OR diameter.

Now Angle PCO=2*35=70.
Thus minor arc PO=(70/360)*2*pi*9=(7/2)*pi

Now Angle QCR=70.
Thus minor arc QR= (7/2)*pi

Hence, minor arc PQ = 9*pi - (7/2)*pi - (7/2)*pi = 2*pi
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narru
 Post subject:
 Post Posted: Wed Jul 16, 2008 11:53 am 
Maverick, you are correct.

when I was solving this question, I tried to find length of 'chord' instead of the 'arc'.
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RonPurewal
 Post subject:
 Post Posted: Sat Jul 19, 2008 4:15 am 
Offline
ManhattanGMAT Staff


Posts: 7146
Maverick wrote:
Imagine the Center C on the OR diameter.

Now Angle PCO=2*35=70.
Thus minor arc PO=(70/360)*2*pi*9=(7/2)*pi

Now Angle QCR=70.
Thus minor arc QR= (7/2)*pi

Hence, minor arc PQ = 9*pi - (7/2)*pi - (7/2)*pi = 2*pi


this works.

if you don't like doing so much math with pi and fractions, you can always find the number of degrees in arc pq first. since angles qpr and pro are both 35 degrees (alternate interior angles), arcs op and qr must both be 70°. therefore, the degree measure of arc pq is 180 - 70 - 70 = 40°.

you can then find the length directly as (40/360)(18pi) = 18pi/9 = 2pi.

not that much more efficient than the solution posted here, but any degree (heh, "degree") of extra efficiency is worth it for the extra time gained.[/list]
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Guest
 Post subject: cool
 Post Posted: Mon Jul 21, 2008 11:07 am 
thanks friends..
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