Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 06:03

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

If the circle in the figure above is centered at the origin of the coo

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56306
If the circle in the figure above is centered at the origin of the coo  [#permalink]

Show Tags

02 Oct 2016, 05:45
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:08) correct 28% (01:38) wrong based on 214 sessions

HideShow timer Statistics

If the circle in the figure above is centered at the origin of the coordinate axes, which of the following coordinates represents a point that lies on the circle?

A. (3,4)
B. (5,5)
C. (1,9)
D. (8,6)
E. (6,6)

Attachment:

T6192.png [ 6.7 KiB | Viewed 3005 times ]

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 3094
If the circle in the figure above is centered at the origin of the coo  [#permalink]

Show Tags

08 Apr 2018, 15:47
3
2
Bunuel wrote:
If the circle in the figure above is centered at the origin of the coordinate axes, which of the following coordinates represents a point that lies on the circle?

A. (3,4)
B. (5,5)
C. (1,9)
D. (8,6)
E. (6,6)
lostnumber wrote:
Can someone explain this to me? I understand the radius is 10 and that you could make a right triangle between X and Y, but I don't understand how that helps you find a point on the circle. Wouldn't all points on the arc be outside of the triangle?

lostnumber , if by "arc" you mean the circumference line, no.
A point lies ON a circle if it lies ON the circumference

Points on a circle

• any point that lies on the circle will
satisfy the equation for the circle (below)

• any point that lies on the circle will
create a right triangle whose hypotenuse = radius

Basic equation of a circle
To determine whether a point lies on a circle,
plug the x- and y-coordinates into the equation

As abhimahna and 0akshay0 mention explicitly,
the basic equation of a circle is

$$x^2 + y^2 = r^2$$

$$x$$ and $$y$$ are coordinates
of a point on the circle
$$r$$ = radius

Basic equation of circle $$<->$$ Pythagorean theorem

Pythagorean theorem, where c = hypotenuse:
$$a^2 + b^2 = c^2$$
Basic equation of circle with center (0,0), r = radius:
$$x^2 + y^2 = r^2$$

x replaces a, y replaces b
and r, radius, replaces c, hypotenuse

Any point (x,y) on this circle therefore
satisfies the equation for THIS circle:
$$x^2 + y^2 = 10^2$$
$$x^2 + y^2 = 100$$

You're looking for x- and y-values
whose squares will sum to 100.

You can plug in until you find the right pair.

Try A. (3,4)

$$3^2 + 4^2 = r^2$$
$$r^2 = 25$$
$$r = 5$$

r must = 10

You can keep plugging in
until you get the correct x- and y- values

See the RHS of diagram.*
All points except D lie INSIDE the circle
Their radii lengths are shorter than 10

OR notice: 6-8-10 = 3-4-5 right triangle

8: 6: 10 = 4x-3x-5x

D's x- and y-coordinates yield lengths
that are a "Pythagorean triplet" triangle

(8, 6) makes a right triangle. See diagram.

Check: do D's coordinates (8,6) satisfy equation?

$$x^2 + y^2 = r^2$$
$$8^2 + 6^2 = r^2$$
$$64 + 36 = r^2$$
$$r^2 = 100$$
$$r = 10$$

That's a match.

Hope that helps

* Look at the green triangle on the left.
The green point is (-6, 8). It, too, satisfies the equation

$$(-6)^2 + 8^2 = r^2$$
$$(36 + 64) = 100 = r^2$$
$$r^2 = 100$$
$$r = 10$$

For more on the equation of a circle, see Bunuel , Circle on a plane , and another site HERE

Attachment:

T6192ed2.png [ 35.27 KiB | Viewed 1365 times ]

_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.

-- Take another look. Take a look around. These are the moments you can't pass by.
General Discussion
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3625
Re: If the circle in the figure above is centered at the origin of the coo  [#permalink]

Show Tags

02 Oct 2016, 06:32
1
2
Bunuel wrote:

If the circle in the figure above is centered at the origin of the coordinate axes, which of the following coordinates represents a point that lies on the circle?

A. (3,4)
B. (5,5)
C. (1,9)
D. (8,6)
E. (6,6)

Attachment:
T6192.png

Radius of the circle shown is 10.

So, equation of the circle can be written as $$x^2 + y^2 = 10^2$$

Now, only point that satisfies this equation is (8,6). Hence, D
_________________
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Manager
Joined: 27 Aug 2014
Posts: 54
Concentration: Strategy, Technology
GMAT 1: 660 Q45 V35
GPA: 3.66
WE: Consulting (Consulting)
Re: If the circle in the figure above is centered at the origin of the coo  [#permalink]

Show Tags

07 Jan 2017, 12:41
Distance from 0 to the the y intercept of the circle is 10. So pick the coordinates whos squares add upto a 100. Since root of 100 = distance from origin = 10.
Manager
Joined: 25 Jun 2016
Posts: 61
GMAT 1: 780 Q51 V46
Re: If the circle in the figure above is centered at the origin of the coo  [#permalink]

Show Tags

07 Jan 2017, 14:53
1
On questions that involve right triangles, you can often save considerable time by looking for the classic Pythagorean triplets (the 3:4:5 classic triangle and its multiples, the 5:12:13 classic triangle and its multiples, etc.)

Here, a radius drawn from the origin to a point on the circle will be the hypotenuse of a right triangle whose legs are given by the coordinates of the point on the circle.

That hypotenuse/radius will have a length 10 (from the picture). A 3:4:5 triangle is the most likely triangle since it is the only very common classic right triangle with a multiple of 5 for the hypotenuse (it's also the most common right triangle on the gmat). If we're going to have a 10 for the longest side, we want the 6:8:10 version of the classic 3:4:5. Answer D satisfies.
Senior Manager
Joined: 19 Apr 2016
Posts: 271
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
Re: If the circle in the figure above is centered at the origin of the coo  [#permalink]

Show Tags

23 Jan 2017, 03:42
Bunuel wrote:

If the circle in the figure above is centered at the origin of the coordinate axes, which of the following coordinates represents a point that lies on the circle?

A. (3,4)
B. (5,5)
C. (1,9)
D. (8,6)
E. (6,6)

Attachment:
T6192.png

From the given figure we have radius = 10
so the equation of the given circle is $$x^2 + y^2 = 10^2$$
only (8,6) satisfies the equation

Hence option D is correct
Intern
Joined: 28 Mar 2018
Posts: 45
Re: If the circle in the figure above is centered at the origin of the coo  [#permalink]

Show Tags

06 Apr 2018, 07:34
Can someone explain this to me? I understand the radius is 10 and that you could make a right triangle between X and Y, but I don't understand how that helps you find a point on the circle. Wouldn't all points on the arc be outside of the triangle?
Intern
Joined: 28 Mar 2018
Posts: 45
Re: If the circle in the figure above is centered at the origin of the coo  [#permalink]

Show Tags

09 Apr 2018, 06:59
1
Thanks so much for the detailed explanation Generis! It turns out this is simply a math formula and concept that I didn't know, so I'll have to add this to my long list of quant topics to study. But your answer was very detailed and I've bookmarked for future reference. I know what I need to study now! Thanks again
Non-Human User
Joined: 09 Sep 2013
Posts: 11719
Re: If the circle in the figure above is centered at the origin of the coo  [#permalink]

Show Tags

12 May 2019, 15:59
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: If the circle in the figure above is centered at the origin of the coo   [#permalink] 12 May 2019, 15:59
Display posts from previous: Sort by