BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Circles

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Quantitative Reasoning |
User avatar
GMAT Instructor
Posts: 1035
Joined: Fri Dec 17, 2010 11:13 am
Location: Los Angeles, CA
Thanked: 474 times
Followed by:365 members

by VivianKerr » Tue Apr 26, 2011 7:04 am
Hi Naveen,

Since PQ and OR are parallel, then we can think of PR as a transversal. When two parallel lines are cut by a transversal (a third line), then all of the acute angles are equal, and all of the obtuse angles are equal.

Following this rule, since angle PRO = 35, then angle QPR = 35.

Angle QPR is called an "inscribed angle" since it's vertex is on the circumference of the circle, and arc QR is called the "intercepted arc".

Easier GMAT questions will put the "inscribed angle"'s vertex at the center of the circle (called a "central angle"). If we know the "central angle" we can usually solve for the arc length using a proportion, since the "central angle" is always a fraction of 360 degrees.

To find the "central angle" of 35 degrees, all we have to do is double it. So the "central angle" that corresponds to the "intercepted arc" has a measure of 70.

Now we can set up a proportion using our knowledge of part/whole:

70/360 = arc QR / 2*pi*r

Again, we can do this because there are 360 degrees total around the centerpoint of a circle, and any arc of a circle can be expressed as a fraction of the circle's total circumference (found by the expression 2*pi*r).

Since the diameter is 18, the radius is 9. Plugging that in:

70/360 = arcQR / 18pi

Now we can cross-multiply to solve:

(70)(18pi) = (360)(arcQR)
1260pi = (360)(arcQR)
3.5pi = arcQR

The answer is C.
Vivian Kerr
GMAT Rockstar, Tutor
https://www.GMATrockstar.com
https://www.yelp.com/biz/gmat-rockstar-los-angeles

Former Kaplan and Grockit instructor, freelance GMAT content creator, now offering affordable, effective, Skype-tutoring for the GMAT at $150/hr. Contact: [email protected]

Thank you for all the "thanks" and "follows"! :-)
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Apr 27, 2011 5:55 am
Hi Vivian,

I think you found the length of arc QR (which is 7pi/2), but the question asks for the length of arc PQ.
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Apr 27, 2011 5:58 am
I thought a graphic might help here.
Attachments
inscribed-central-angles.PNG
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1