Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 563 reviewsTarget Test Prep

GMAT Prep Geometry Question

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 66
Joined: Sat Sep 29, 2007 7:17 pm
Thanked: 5 times
GMAT Score:660
by ssy » Mon Oct 22, 2007 6:54 am
In the circle in the image attached, PQ is parallel to diameter OR. OR has length 18. What is the length of minor arc PQ?

2pi
(9pi)/4
(7pi)/2
(9p)/2
3pi

Ans 2pi[/img]
You do not have the required permissions to view the files attached to this post.
Top
Join the discussion
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 258
Joined: Mon Aug 27, 2007 12:43 pm
Thanked: 15 times

by ri2007 » Mon Oct 22, 2007 7:04 am
Diameter is 18 so circumference of semi circle = 18 pi /2 = 9 pi

PQ ll OR so angle R = angle P = 35

so arc OP = arc QR = 35 * 2 = 70

so arc PQ = 180 - ( arc OP + arc QR) = 40 deg

Since 180 deg corresponds to 9 pi

40 corresponds to 2 pi ( cross multiplication)
Top
Join the discussion
Senior | Next Rank: 100 Posts
Posts: 66
Joined: Sat Sep 29, 2007 7:17 pm
Thanked: 5 times
GMAT Score:660

by ssy » Mon Oct 22, 2007 7:13 am
Thank you ri2007 but I am still confused.

Isn't the circumference of the semicircle (pi)(radius)+2pi, so the circumference in this case is [(pi)(9)+18]

Also, can you please explain the following steps

"so arc OP = arc QR = 35 * 2 = 70

so arc PQ = 180 - ( arc OP + arc QR) = 40 deg"

Thanks very much.
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 258
Joined: Mon Aug 27, 2007 12:43 pm
Thanked: 15 times

by ri2007 » Mon Oct 22, 2007 7:34 am
Point 1) Circumference is 2 pi r or 2 pi d where d is the diameter,

Point 2) since PQ ll OR and angle R & angle P are the internal angles formed by the transversal - internal angles are equal.

Point 3) semicircle = 180 degrees
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 315
Joined: Thu Aug 17, 2006 10:43 pm
Thanked: 23 times

by Suyog » Mon Oct 22, 2007 1:55 pm
I'm also lil confused!
if angle R = 35 then how arc OP = 70 ??
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 258
Joined: Mon Aug 27, 2007 12:43 pm
Thanked: 15 times

by ri2007 » Mon Oct 22, 2007 2:21 pm
Suyog wrote:I'm also lil confused!
if angle R = 35 then how arc OP = 70 ??
Its a geometry rule of inscribed angle
minor arc is 2* inscribed angle
Top
Join the discussion
Senior | Next Rank: 100 Posts
Posts: 66
Joined: Sat Sep 29, 2007 7:17 pm
Thanked: 5 times
GMAT Score:660

by ssy » Tue Oct 23, 2007 4:40 am
Sorry I am still confused.

Point 1) Do you mean the circumference of a semi circle because isn't the circumference of the semi circle (pi)(radius)+diameter?

https://sg.answers.yahoo.com/question/in ... n6D&show=7

Point 3) How can you subtract the length of the two arcs from 180 degrees?
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 258
Joined: Mon Aug 27, 2007 12:43 pm
Thanked: 15 times

by ri2007 » Tue Oct 23, 2007 6:03 am
ssy wrote:Sorry I am still confused.

Point 1) Do you mean the circumference of a semi circle because isn't the circumference of the semi circle (pi)(radius)+diameter?

https://sg.answers.yahoo.com/question/in ... n6D&show=7

Point 3) How can you subtract the length of the two arcs from 180 degrees?
I have made one typing error earlier in explaining the formula for circumference of circle it is 2 pi r or pi d no 2 pi d as typed earlier by mistake. This is the right formula

THis questions is either from OG or Kaplan. They have also give an explaination. You can check it
Top
Join the discussion
Senior | Next Rank: 100 Posts
Posts: 69
Joined: Sat Sep 15, 2007 1:54 am

by manasi_sh » Tue Oct 23, 2007 7:41 am
Also there is a formula for Length of Arc:
degree measure(here 40)/360* 2 PI R(circumference formula)
so over here Arc PQ = 40/360 *(2PI*9) = 2PI(ANS)
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 174
Joined: Mon Mar 26, 2007 5:51 am
Thanked: 1 times

by 800GMAT » Fri Nov 02, 2007 2:49 pm
Some relevant properties:
You do not have the required permissions to view the files attached to this post.
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 106
Joined: Tue Oct 09, 2007 12:25 pm
Thanked: 1 times

by xcise_science » Tue Nov 27, 2007 11:00 am
can someone explain this part to me:

Since 180 deg corresponds to 9 pi
40 corresponds to 2 pi ( cross multiplication)

I'm not clear on how/why 180 corresponds to 9pi.

thanks
Top
Join the discussion
2009 Beat The GMAT Scholarship Winner
Posts: 182
Joined: Sat Mar 22, 2008 7:35 pmFollowed by: 2 members
Thanked: 3 times
GMAT Score:700+

by gkumar » Mon Oct 19, 2009 11:42 am
I'm still unclear why the degree measures of minor arcs PAO and QAR are equal. I understand why PAO has a measure 70 degrees, but not why QAR has a measure of 70 degrees. Can you please explain via a proof or some other explanation on how angles QAR = PAO?

Here's what I know so far (see attachment)
You do not have the required permissions to view the files attached to this post.
Top
Join the discussion
User avatar
GMAT Instructor
Posts: 3224
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Mon Oct 19, 2009 12:24 pm
gkumar wrote:I'm still unclear why the degree measures of minor arcs PAO and QAR are equal. I understand why PAO has a measure 70 degrees, but not why QAR has a measure of 70 degrees. Can you please explain via a proof or some other explanation on how angles QAR = PAO?

Here's what I know so far (see attachment)
Hi!

We know that angle APQ is 70 degrees (35+35). We also know that triangle APQ is isosceles, since both AP and AQ are radii of the circle.

Therefore, angle AQP is also 70 degrees, leaving 40 degrees for central angle PAQ.

So, PAO is 70 and PAQ is 40. 180 - 110 = 70 degrees left over for angle QAR.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
2009 Beat The GMAT Scholarship Winner
Posts: 182
Joined: Sat Mar 22, 2008 7:35 pmFollowed by: 2 members
Thanked: 3 times
GMAT Score:700+

by gkumar » Mon Oct 19, 2009 12:35 pm
Thanks Stuart! I forgot about the isoceles triangle part. All of these angles are hard to keep track and manage under 2 minutes. Is it possible to use Symmetry to assume that QAR is automatically equal to PAO?
Top
Join the discussion
User avatar
GMAT Instructor
Posts: 3224
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Mon Oct 19, 2009 12:39 pm
gkumar wrote:Thanks Stuart! I forgot about the isoceles triangle part. All of these angles are hard to keep track and manage under 2 minutes. Is it possible to use Symmetry to assume that QAR is automatically equal to PAO?
We need to careful not to assume that everything will be symmetrical, so it's not a safe bet.

However, the fact that all triangles radiating out from the centre of a circle are isosceles is commonly tested, so be on the lookout for such situations.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion