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 →

Rectangle inscribed in a circle

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Mon May 10, 2010 11:55 pm
Thanked: 4 times
by surajgarg » Fri Aug 06, 2010 12:25 pm
In the xy-coordinate system, rectangle ABCD is inscribed within a circle having the equation x^2 + y^2 = 25. Line segment AC is a diagonal of the rectangle and lies on the x-axis. Vertex B lies in quadrant II and vertex D lies in quadrant IV. If side BC lies on line y=3x+15, what is the area of rectangle ABCD?

A. 15
B. 30
C. 40
D. 45
E. 50
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 759
Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members
Thanked: 85 times

by clock60 » Fri Aug 06, 2010 2:25 pm
i got B-30
reasoning
at first let us find the point where line y=3x+15 intersect with the circle x^2+y^2=5^2 with radiu=5 ( as circle with the center in the origin is given wiith the equation x^2+y^2=R^2)
x^2+(3x+15)^2=25
solving and simplifing
x^2+9x+20=0
x1=-5,x2=-4. we need here x2=-4. ( as -5 already given in the query)
insert x2=-4 in the y=3x+15,
y=-12+15=3
here y=3 is the height of triangle ABC and we can find its area
S=1/2*10(base)*3(height)=15
our rectangle consists of two equal triangles with area =15
so area of rectangle ABCD=2*15=30
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 51
Joined: Mon May 10, 2010 11:55 pm
Thanked: 4 times

by surajgarg » Fri Aug 06, 2010 8:48 pm
clock60 wrote:i got B-30
reasoning
at first let us find the point where line y=3x+15 intersect with the circle x^2+y^2=5^2 with radiu=5 ( as circle with the center in the origin is given wiith the equation x^2+y^2=R^2)
x^2+(3x+15)^2=25
solving and simplifing
x^2+9x+20=0
x1=-5,x2=-4. we need here x2=-4. ( as -5 already given in the query)
insert x2=-4 in the y=3x+15,
y=-12+15=3
here y=3 is the height of triangle ABC and we can find its area
S=1/2*10(base)*3(height)=15
our rectangle consists of two equal triangles with area =15
so area of rectangle ABCD=2*15=30
Thanks, I overlooked the fact that the line BC will intersect the circle :D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 516
Joined: Mon Nov 02, 2009 6:42 amFollowed by: 1 member
Location: Mumbai
Thanked: 14 times
GMAT Score:710

by ankurmit » Sun Aug 08, 2010 6:02 am
Can anyone elaborate it with a figure..I am not able to draw it..
--------
Ankur mittal
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Fri Aug 06, 2010 11:12 pm

by zareentaj » Mon Aug 09, 2010 11:16 pm
clock60 wrote:i got B-30
reasoning
at first let us find the point where line y=3x+15 intersect with the circle x^2+y^2=5^2 with radiu=5 ( as circle with the center in the origin is given wiith the equation x^2+y^2=R^2)
x^2+(3x+15)^2=25
solving and simplifing
x^2+9x+20=0
x1=-5,x2=-4. we need here x2=-4. ( as -5 already given in the query)
insert x2=-4 in the y=3x+15,
y=-12+15=3
here y=3 is the height of triangle ABC and we can find its area
S=1/2*10(base)*3(height)=15
our rectangle consists of two equal triangles with area =15
so area of rectangle ABCD=2*15=30
Thanks clock60. for solve this question ,i got idea for this type of questions.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1