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

 It is currently 17 Oct 2018, 15:41

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

Author Message
TAGS:

### Hide Tags

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

### Show Tags

01 Jun 2017, 00:15
6
00:00

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
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1381
Location: Viet Nam
In a rectangular coordinate plane, AB is the diameter of a circle and  [#permalink]

### Show Tags

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

### Show Tags

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.
• C: Wrong Y
• D: Wrong Y
• E: Wrong Y

Time: 1:46
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