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 →

Circle

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1560
Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members
Thanked: 137 times

by thephoenix » Wed May 05, 2010 12:13 am
IMO B
let the centre be x,y
eqn 1(dist b/n center and point 1,2) is x
x^2+1-2x+y^2+4-4y
similarly eqn2 x^2+y^2+25+4-10y-4x
eqn3 x^2+y^2+25+16-10x-8y

by equating eqn 1 and 2 we get x+3y=12
and by equating eqn2 and 3 we get 3x-y=6solving x=y=3
radius=sqrt5 and dia=sqrt20
Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 526
Joined: Sat Feb 21, 2009 11:47 pm
Location: India
Thanked: 68 times
GMAT Score:680

by harshavardhanc » Wed May 05, 2010 12:16 am
getso wrote:If a circle passes through points (1, 2)(2,5),and (5,4) what is the diameter of the circle?
(A) sqrt(18)
(B) sqrt(20)
(C) sqrt(22)
(D) sqrt(26)
(E) sqrt(30)
couldn't find a shorter way, but to solve the equations. :(

IMO B.

Anyone with a short-cut ?
Regards,
Harsha
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 576
Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member
Thanked: 97 times

by liferocks » Wed May 05, 2010 3:11 am
the three points (1, 2)(2,5),and (5,4) form a right angle triangle

distance between (1, 2)(2,5)= V10
distance between (2,5)(5,4)= V10
distance between (1, 2)(5,4)= V20
hence diameter = length of hypotenuse =sqrt(20)

option B
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 610
Joined: Fri Jan 15, 2010 12:33 amFollowed by: 2 members
Thanked: 47 times

by kstv » Wed May 05, 2010 3:37 am
If you plot the point on a graph
A (1,2) , B ( 2,5) and C ( 5,4) it becomes clear AB is perpendicular to BC.
Not convinced, slope of AB*slope of BC = -1
(5-2)/(2-1) x(5-4)/(2-5)=-1
Since the circle touch all the points of the triangle ABC and <ABC is 90°
AC has to be the diameter.
AC² = (5-1)²+(4-2)² = 20
IMO B.

Frankly if ABC is not a rt. angle triangle finding the diameter will test concepts beyond the scope of GMAT.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 526
Joined: Sat Feb 21, 2009 11:47 pm
Location: India
Thanked: 68 times
GMAT Score:680

by harshavardhanc » Wed May 05, 2010 3:47 am
liferocks wrote:the three points (1, 2)(2,5),and (5,4) form a right angle triangle

distance between (1, 2)(2,5)= V10
distance between (2,5)(5,4)= V10
distance between (1, 2)(5,4)= V20
hence diameter = length of hypotenuse =sqrt(20)

option B
naaaaaaice! thanks buddy!
Regards,
Harsha
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2326
Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members
Thanked: 173 times
GMAT Score:710

by gmatmachoman » Wed May 05, 2010 4:30 am
liferocks wrote:the three points (1, 2)(2,5),and (5,4) form a right angle triangle

distance between (1, 2)(2,5)= V10
distance between (2,5)(5,4)= V10
distance between (1, 2)(5,4)= V20
hence diameter = length of hypotenuse =sqrt(20)

option B
https://www.codecogs.com/reference/maths ... circle.php


Guys, i think are we writing olympiads....?? hehehe!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 141
Joined: Sat Feb 28, 2009 8:19 am
Thanked: 1 times

by getso » Sat May 08, 2010 7:09 pm
kstv wrote:If you plot the point on a graph
A (1,2) , B ( 2,5) and C ( 5,4) it becomes clear AB is perpendicular to BC.
Not convinced, slope of AB*slope of BC = -1
(5-2)/(2-1) x(5-4)/(2-5)=-1
Since the circle touch all the points of the triangle ABC and <ABC is 90°
AC has to be the diameter.
AC² = (5-1)²+(4-2)² = 20
IMO B.

Frankly if ABC is not a rt. angle triangle finding the diameter will test concepts beyond the scope of GMAT.
Thanks for the wonderful explaination..
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members
Location: Gandhinagar
Thanked: 41 times

by shashank.ism » Sat May 08, 2010 7:21 pm
kstv wrote:If you plot the point on a graph
A (1,2) , B ( 2,5) and C ( 5,4) it becomes clear AB is perpendicular to BC.
Not convinced, slope of AB*slope of BC = -1
(5-2)/(2-1) x(5-4)/(2-5)=-1
Since the circle touch all the points of the triangle ABC and <ABC is 90°
AC has to be the diameter.
AC² = (5-1)²+(4-2)² = 20
IMO B.

Frankly if ABC is not a rt. angle triangle finding the diameter will test concepts beyond the scope of GMAT.
nice one..
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1