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

 It is currently 20 Mar 2019, 06:57

### 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

# A and B are the end points of the longest line that can be drawn in a

Author Message
TAGS:

### Hide Tags

Senior RC Moderator
Status: Preparing GMAT
Joined: 02 Nov 2016
Posts: 2422
Location: Pakistan
GPA: 3.39
A and B are the end points of the longest line that can be drawn in a  [#permalink]

### Show Tags

24 Feb 2017, 07:46
6
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:19) correct 32% (02:01) wrong based on 71 sessions

### HideShow timer Statistics

A and B are the end points of the longest line that can be drawn in a circle with center X. If C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC?

(A) 9/2
(B) 9
(C) 6 + 3 $$\sqrt{3}$$
(D) 9 + 3 $$\sqrt{3}$$
(E) 9 $$\sqrt{3}$$

_________________

New Project RC Butler 2019 - Practice 2 RC Passages Everyday
Final days of the GMAT Exam? => All GMAT Flashcards.
This Post Helps = Press +1 Kudos
Best of Luck on the GMAT!!

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4486
Re: A and B are the end points of the longest line that can be drawn in a  [#permalink]

### Show Tags

24 Feb 2017, 12:19
2
A and B are the end points of the longest line that can be drawn in a circle with center X. If C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC?

(A) 9/2
(B) 9
(C) 6 + 3 $$\sqrt{3}$$
(D) 9 + 3 $$\sqrt{3}$$
(E) 9 $$\sqrt{3}$$

I'm happy to respond.

First, "the longest line that can be drawn in a circle" = the diameter. We know AB is a diameter.

X is the center, so AX & BC are radii. AC is a chord that is equal in length to the radius, and XC is another radius, so ACX is an equilateral triangle, with three 60 degree angles. Let's look at a diagram:
Attachment:

circle X with triangle ABC.png [ 77.94 KiB | Viewed 1308 times ]

The next piece we need is that any triangle with three vertices on a circle that has a diameter a side is a right triangle. Another way to say that is that any angle that intersects an arc of a semicircle is a right angle. See the "special case" in this blog article:
Inscribed and Circumscribed Circles and Polygons on the GMAT
Thus, ABC is a 30-60-90 triangle. The ratios in this triangle should be familiar. See this blog if they are not:
The GMAT’s Favorite Triangles
We know AC = 3.
We know AB = AX + BX = 6
The third side is the side opposite the 60 degree angle in the 30-60-90 triangle. This is $$\sqrt{3}$$ times the shortest side. Thus:
BC = $$3\sqrt{3}$$

perimeter of ABC = AC + AB + BC = $$9 + 3\sqrt{3}$$

OA = (D)

Does all this make sense?
Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Non-Human User
Joined: 09 Sep 2013
Posts: 10152
Re: A and B are the end points of the longest line that can be drawn in a  [#permalink]

### Show Tags

16 Feb 2019, 02:49
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: A and B are the end points of the longest line that can be drawn in a   [#permalink] 16 Feb 2019, 02:49
Display posts from previous: Sort by