GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Oct 2018, 15:41

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

In a rectangular coordinate plane, AB is the diameter of a circle and

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
S
Joined: 14 Sep 2015
Posts: 65
Location: India
GMAT 1: 700 Q45 V40
GPA: 3.41
GMAT ToolKit User
In a rectangular coordinate plane, AB is the diameter of a circle and  [#permalink]

Show Tags

New post 01 Jun 2017, 00:15
6
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

72% (02:18) correct 28% (02:04) wrong based on 79 sessions

HideShow timer Statistics

In a rectangular coordinate plane, AB is the diameter of a circle and point C lies on the circle. If the coordinates of points A and B are (-1,0) and (5,0), and the area of triangle ABC is \(6\sqrt{2}\)square units, which of the following can be the coordinates of point C?



A. (0, 2\(\sqrt{2}\))
B. (1, 2\(\sqrt{2}\))
C. (\(\sqrt{2}\),2)
D. (2,\(\sqrt{2}\))
E. (2\(\sqrt{2}\),1)
Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1381
Location: Viet Nam
GMAT ToolKit User Premium Member
In a rectangular coordinate plane, AB is the diameter of a circle and  [#permalink]

Show Tags

New post 01 Jun 2017, 01:40
2
niteshwaghray wrote:
In a rectangular coordinate plane, AB is the diameter of a circle and point C lies on the circle. If the coordinates of points A and B are (-1,0) and (5,0), and the area of triangle ABC is \(6\sqrt{2}\)square units, which of the following can be the coordinates of point C?

A. (0, 2\(\sqrt{2}\))
B. (1, 2\(\sqrt{2}\))
C. (\(\sqrt{2}\),2)
D. (2,\(\sqrt{2}\))
E. (2\(\sqrt{2}\),1)


Attachment:
Capture.PNG
Capture.PNG [ 12.32 KiB | Viewed 990 times ]

We have \(AB=6 \implies R = 3\).

\(I\) is the center of that circle, then we have \(I(2,0)\)

The equation of that circle is \((I): \; \; (x-2)^2 + y^2 = 3^2\)

The coordinates of \(C(x_C, y_C)\). We have \((x_C-2)^2 + y_C^2 = 9\)

Also, we have
\(S_{ABC}=6\sqrt{2} \implies \frac{AB \times |y_C|}{2}=6\sqrt{2} \\
\implies |y_C|=2\sqrt{2} \implies y_C^2=8 \)
\(\implies (x_C-2)^2 = 1 \implies x_C = 3\) or \(x_C = 1\).

Only choice B fits the roots. B is the correct answer.
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Intern
Intern
avatar
B
Joined: 03 Sep 2018
Posts: 5
In a rectangular coordinate plane, AB is the diameter of a circle and  [#permalink]

Show Tags

New post 25 Sep 2018, 11:05
1
Analysis (51 seconds): Draw out a rough estimation of the coordinate plane, mark the points and draw a circle. Notice that I can use the area of a triangle to get a value for Y for point C.

Strategy: Find Y, Eliminate

Find Y (35 seconds)
\(Ta = \frac{1}{2}*b*h\)

\(\frac{1}{2}*6*h = 6\sqrt{2}\)

\(3*h = 6\sqrt{2}\)

\(Y = 6\sqrt{2} / 3\)

\(Y = 2\sqrt{2}\)

Eliminate (20 seconds)
  • A: With only two choices left, logically it can only be the one closest to the centre of the circle so eliminate A.
  • B: Correct Answer
  • C: Wrong Y
  • D: Wrong Y
  • E: Wrong Y

Answer: B
Time: 1:46
GMAT Club Bot
In a rectangular coordinate plane, AB is the diameter of a circle and &nbs [#permalink] 25 Sep 2018, 11:05
Display posts from previous: Sort by

In a rectangular coordinate plane, AB is the diameter of a circle and

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.