| View previous topic :: View next topic |
| Author |
Message |
sudhirsk
Just gettin' started!
Joined: 27 Nov 2006
Posts: 15
Thanks given: 0
Thanked 0 times in 0 posts
|
 Posted: Mon Jul 02, 2007 8:44 pm Post subject: GMAT Prep Question |
 |
|
Please explain how to solve this.
|
|
| Back to top |
|
 |
|
|
jayhawk2001
Moderator
Joined: 28 Jan 2007
Posts: 789
Thanks given: 0
Thanked 11 times in 11 posts
Location: Silicon valley, California
|
| Posted: Mon Jul 02, 2007 10:21 pm Post subject: |
|
|
The key here is that the minor arc OP is twice the measure
of the inscribed angle (PRO). So, arc OP = 70 / 360 * 2* pi * r
Similarly, if you draw a line OQ, it will subtend the same angle and hence
QR will be of the same measure i.e. 70 / 360 * 2* pi * r.
So, arc OP + arc QR = 70 / 360 * 2*pi*9 * 2 = 7*pi
Arc length OR = 9*pi
So, minor arc PQ = 9*pi - 7*pi = 2*pi
This is actually a question in OG-11.
|
|
| Back to top |
|
|
moneyman
GMAT Destroyer!
Joined: 03 Mar 2007
Posts: 359
Thanks given: 3
Thanked 3 times in 3 posts
|
| Posted: Tue Jul 03, 2007 1:43 am Post subject: |
|
|
Hi jayhawk..
Just wanted to know..How can you be sure that arc QR wold have the same inscribed angle??
_________________
Maxx |
|
| Back to top |
|
|
jayhawk2001
Moderator
Joined: 28 Jan 2007
Posts: 789
Thanks given: 0
Thanked 11 times in 11 posts
Location: Silicon valley, California
|
| Posted: Tue Jul 03, 2007 9:36 pm Post subject: |
|
|
| moneyman wrote: | Hi jayhawk..
Just wanted to know..How can you be sure that arc QR wold have the same inscribed angle?? |
We are given that line PQ is parallel to the diameter. So, the corresponding angles PRO and ROQ will be of the same value.
Put another way, if you draw a line from P to center of the circle (lets
call it C) you will get a triangle PRC. Since PC = CR = radius, angles
RPC and angles CRP will be equal = 35 degrees. So, angle PCR = 110
degrees and so angle PCO = 70 degrees.
Similarly, angle QCR = 70 degrees. The remaining 180 - 70 - 70 is the
angle subtended by arc PQ which is 40 degrees.
We can hence calculate 40 / 360 * 2 * pi * 9 = 2 * pi
|
|
| Back to top |
|
|
moneyman
GMAT Destroyer!
Joined: 03 Mar 2007
Posts: 359
Thanks given: 3
Thanked 3 times in 3 posts
|
| Posted: Thu Jul 05, 2007 3:53 am Post subject: |
|
|
Thanks Jay..Was very helpful..Your explanation rocks..
_________________
Maxx |
|
| Back to top |
|
|
|
|
|
