GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 May 2020, 07:22

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In the xy-coordinate system, rectangle ABCD is inscribed within a circ

Author Message
TAGS:

### Hide Tags

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10442
Location: Pune, India
Re: In the xy-coordinate system, rectangle ABCD is inscribed within a circ  [#permalink]

### Show Tags

04 Apr 2018, 03:54
2
gmatmo wrote:

thanks for this awesome approach, but how do you know that -4,3 has to lie on the circle, why isn't it (-3,6)?

The distance of any point lying on the circle from (0, 0) must be 5 (since the radius of the circle is 5).
(-4, 3) is at a distance of 5 from (0, 0) but (-3, 6) is not (even though it lies on the line). It will not lie on the circle.
_________________
Karishma
Veritas Prep GMAT Instructor

Director
Joined: 04 Aug 2010
Posts: 599
Schools: Dartmouth College
Re: In the xy-coordinate system, rectangle ABCD is inscribed within a circ  [#permalink]

### Show Tags

15 May 2019, 02:47
AnkitK wrote:
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

x²+y² = r² is the equation for a circle with its center at the origin and a radius of r.
Thus, x²+y² = 25 is a circle with a center at the origin and a radius of 5.
The information in the prompt yields the following figure:

OB is a radius and thus has a length of 5.
Given the GMAT's love of special triangles, it is likely that triangle BOE is a 3-4-5 triangle, implying that B is located either at (-3, 4) or (-4, 3).
B lies on the line y=3x+15.
If we plug x=-4 into y=3x+15, we get y=3, implying that (-4, 3) lies on y=3x+15.
Thus, B is located at (-4, 3).

Since BE=3, the area of triangle ABC = (1/2)bh = (1/2)(CA)(BE) = (1/2)(10)(3) = 15.
Since the triangle ABC is 1/2 of rectangle ABCD, we get:
ABCD=30.

_________________
GMAT and GRE Tutor
New York, NY

Available for tutoring in NYC and long-distance.
Intern
Joined: 08 Apr 2019
Posts: 9
Re: In the xy-coordinate system, rectangle ABCD is inscribed within a circ  [#permalink]

### Show Tags

10 Aug 2019, 09:00
We don't actually need to find the value of AB BC and AC. Since Point B is perpendicular to AC the area of the rectangle can simply be 3*10=30
CEO
Joined: 03 Jun 2019
Posts: 2889
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)
In the xy-coordinate system, rectangle ABCD is inscribed within a circ  [#permalink]

### Show Tags

24 Sep 2019, 09:11
AnkitK wrote:
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

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?

Point B
x^2 + (3x+15)^2 = 25
x^2 + 9x^2 + 90x +225 = 25
10x^2 + 90x + 200 = 0
x^2 + 9x + 20 = 0
(x+5)(x+4) = 0
x = -5 or x = -4
(x,y) = {(-5,0),(-4,3)}
Since point B lies in II quadrant
(x,y) = (-4,3)
Area of ABC = 1/2 * 10 * 3 = 15
Area of ABCD = 15*2 = 30

IMO B
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Non-Human User
Joined: 09 Sep 2013
Posts: 14969
Re: In the xy-coordinate system, rectangle ABCD is inscribed  [#permalink]

### Show Tags

21 Dec 2019, 07:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In the xy-coordinate system, rectangle ABCD is inscribed   [#permalink] 21 Dec 2019, 07:44

Go to page   Previous    1   2   [ 25 posts ]