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

 It is currently 22 Jan 2020, 00:20 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Circle ABCD in the diagram above is defined by the equation x2+y2=25.

Author Message
TAGS:

### Hide Tags

Senior Manager  Joined: 12 Aug 2015
Posts: 279
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags

3
23 00:00

Difficulty:   35% (medium)

Question Stats: 75% (02:25) correct 25% (02:46) wrong based on 276 sessions

### HideShow timer Statistics Circle ABCD in the diagram above is defined by the equation x^2+y^2=25. Line segment EF is defined by the equation 3y=4x+25 and is tangent to circle ABCD at exactly one point. What is the point of tangency?

A. (–4, 3)
B. (–3, 4)
C. (–4, 7/2)
D. (–7/2, 3)
E. (–4, 4)

Attachment: Geometry_Img69.png [ 11.01 KiB | Viewed 6338 times ]
CEO  S
Joined: 20 Mar 2014
Posts: 2549
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags

6
10
Circle ABCD in the diagram above is defined by the equation x^2+y^2=25. Line segment EF is defined by the equation 3y=4x+25 and is tangent to circle ABCD at exactly one point. What is the point of tangency?

A. (–4, 3)
B. (–3, 4)
C. (–4, 7/2)
D. (–7/2, 3)
E. (–4, 4)

Property of 2 mutually perpendicular lines with slopes m1 and m2 ---> m1*m2=-1

Also, the radius drawn from the center of a circle to the point of tangency, is perpendicular to the tangent at the point of tangency.

Thus, equation of line perpendicular to 3y=4x+25 (slope = 4/3)---> y = mx+c with m*(4/3)=-1---> m = -3/4 and it passes through (0,0) giving you c=0 .

Thus the equation of line perpendicular to the given line ---> y = -3/4 * x . Now solve this equation with 3y=4x+25 to get the point of tangency as (-4,3)

Thus, A is the correct answer.
##### General Discussion
Intern  Joined: 26 Aug 2014
Posts: 42
GMAT 1: 650 Q49 V30
GMAT 2: 650 Q49 V31
WE: Programming (Computer Software)
Re: Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags

2
We are given the equation of a line: 3y = 4x + 25 => y = (4/3)x + 25/3
Substituting the value of y in the equation of circle, we get:
x^2 + [ (4/3)x + 25/3 ]^2 = 25
=> x^2 + (16/9)x^2 + (200/9)x + 625/9 = 25
Multiplying by 9 on both sides,

9x^2 + 16x^2 + 200x + 625 = 225
25x^2 + 200x + 400 = 0
x^2 + 8x + 16 = 0

This gives us the value of x = -4
Substituting this value in the equation of line we get,
3y = 4*(-4) + 25 = -16 + 25 = -9
So, y = -3
And out point is (x,y) = (-4,-3)

Ans: A.
Retired Moderator V
Joined: 22 Jun 2014
Posts: 1087
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Re: Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags

3
The point of tangency would satisfy both the equations.

Only (–4, 3) does that. Beware of choice B Option A is the correct choice!
_________________
Current Student S
Status: MBA Candidate Class of 2020
Joined: 10 Jan 2016
Posts: 102
Location: India
Concentration: Operations, Strategy
GMAT 1: 620 Q47 V29
GMAT 2: 670 Q50 V31
GPA: 4
Re: Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags

2
Point should satisfy both the equations i.e, for circle and the line. Plug in the values to get the answers. Its A.
Manager  S
Joined: 17 Aug 2015
Posts: 96
Re: Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags

1
Great explanations all there by intelligent folks. I just looked up the coordinates That also serves some hints
Director  S
Joined: 12 Nov 2016
Posts: 691
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags Circle ABCD in the diagram above is defined by the equation x^2+y^2=25. Line segment EF is defined by the equation 3y=4x+25 and is tangent to circle ABCD at exactly one point. What is the point of tangency?

A. (–4, 3)
B. (–3, 4)
C. (–4, 7/2)
D. (–7/2, 3)
E. (–4, 4)

Attachment:
Geometry_Img69.png

There's a couple of formulas we should have at our disposal in order to solve this question; remember that the slope of the tangent line is the negative reciprocal of the slope of the radius of the circle. Well, we know the center of this circle (0,0). Hence

(x-0)^2 + (y-0)^2 = 25

The two values of x and y must satisfy this equation and also the equation 3y= 4x + 25

Thus

"A"
Retired Moderator P
Joined: 19 Mar 2014
Posts: 912
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags

1 Circle ABCD in the diagram above is defined by the equation x^2+y^2=25. Line segment EF is defined by the equation 3y=4x+25 and is tangent to circle ABCD at exactly one point. What is the point of tangency?

A. (–4, 3)
B. (–3, 4)
C. (–4, 7/2)
D. (–7/2, 3)
E. (–4, 4)

A point if tangent would satisfy both the equations of line and circle

$$x^2+y^2=25$$ and $$3y=4x+25$$

The only point from the options that satisfy the equation is A $$(–4, 3)$$

_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Manager  S
Joined: 06 Jun 2013
Posts: 147
Location: India
Concentration: Finance, Economics
Schools: Tuck
GMAT 1: 640 Q49 V30
GPA: 3.6
WE: Engineering (Computer Software)
Re: Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags

1
as the point of tangency is a common point, it must satisfy both the equations.

only option A and B satisfy the circle equation n this means these two points lie on the circumference of the circle.

now we can get the right answer by putting the values of the x and y co-ordinates on the tangent equation.

only option A satisfies this equation.
Non-Human User Joined: 09 Sep 2013
Posts: 13993
Re: Circle ABCD in the diagram above is defined by the equation x2+y2=25.  [#permalink]

### Show Tags

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: Circle ABCD in the diagram above is defined by the equation x2+y2=25.   [#permalink] 07 Aug 2019, 06:48
Display posts from previous: Sort by

# Circle ABCD in the diagram above is defined by the equation x2+y2=25.  