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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Center of the circle

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members
Thanked: 11 times
by gmattesttaker2 » Sun Dec 01, 2013 12:51 pm
Hello,

Can you please assist with this:

Point P is inside circle X. If A, B, and C are three different points on the
circumference of circle X, is point P the center of circle X?

(1) PA = PB
(2) PA = PC

OA: E

I was thinking that it should be D since for PA to be equal to PB or PC each has to be the radius. Can you please assist?

Thanks,
Sri
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Sun Dec 01, 2013 7:41 pm
Hi Sri,

This DS question will likely be made easier IF you draw some pictures. I'm going to offer some hints and then let you try to solve this problem again.

The "obvious" possibility is that P is the center of the circle. Try drawing that picture with P, A and B (with A and B on the circumference of the circle). Next, pick a point for P OTHER than the center of the circle; could you draw an A and B in such a way that PA and PB would be the same length? Now try drawing a picture with P, A, B and C. These drawings will provide you with the proof that the correct answer is as listed.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Sun Dec 01, 2013 11:31 pm
I think the OA is wrong - a point inside a circle that is equidistant from three points on the circumference (i.e. if PA = PB = PC, as we have here) should be the center.

I'll link you to a nice proof at https://www.artsofliberty.org/sites/defa ... er%203.pdf and take a screenshot of part of the proof:

Image

Image

An easy (GMATy) way of thinking about it, however, is to consider what you have when you take the two statements together. If PA = PB = PC, then you have SOME circle centered at P that goes to A, B, and C, with PA, PB, and PC each the radius of that circle. But A, B, and C are ALSO supposedly on the circumference of some "other" circle that isn't centered at P ... and how can that be? (Try visualizing it and it should hopefully make sense.)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1