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

It is currently 21 Sep 2018, 04:58

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 the figure above, O is the center of the circle. Line AB intersects

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49298
In the figure above, O is the center of the circle. Line AB intersects  [#permalink]

Show Tags

New post 23 Nov 2017, 23:19
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (01:30) correct 28% (00:53) wrong based on 50 sessions

HideShow timer Statistics

Image
In the figure above, O is the center of the circle. Line AB intersects the circle only at point B, and line DC intersects the circle only at point C. If the circle has radius of 2, then AC =

(A) 4
(B) 2√2
(C) 4 + √2
(D) 4 + √3
(E) 2 + 2√2


Attachment:
2017-11-23_2025_001.png
2017-11-23_2025_001.png [ 8.65 KiB | Viewed 1192 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 29 Aug 2016
Posts: 33
GMAT ToolKit User
Re: In the figure above, O is the center of the circle. Line AB intersects  [#permalink]

Show Tags

New post 24 Nov 2017, 01:27
E.

Produce OB and it shall make a right angle at point of contact.
Triangle ABO will be right and isosceles.

AO can be found from pythagoras theorem.

AO+radius is the answer.


Sent from my iPhone using GMAT Club Forum
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8283
Location: Pune, India
Re: In the figure above, O is the center of the circle. Line AB intersects  [#permalink]

Show Tags

New post 24 Nov 2017, 02:16
Bunuel wrote:
Image
In the figure above, O is the center of the circle. Line AB intersects the circle only at point B, and line DC intersects the circle only at point C. If the circle has radius of 2, then AC =

(A) 4
(B) 2√2
(C) 4 + √2
(D) 4 + √3
(E) 2 + 2√2


Attachment:
2017-11-23_2025_001.png


OB is the radius of the circle and AB is the tangent. Radius is perpendicular to tangent at the point of intersection. In triangle OBA, angle A is 45 degrees, angle ABO is 90 degrees and hence angle BOA is also 45 degrees. This is a 45-45-90 triangle in which ratio of the sides will be \(1:1:\sqrt{2}\)
Using pythagorean theorem, AO \(= 2\sqrt{2}\)

AC = AO + OC = \(2\sqrt{2} + 2\)

Answer (E)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
User avatar
B
Joined: 16 Oct 2017
Posts: 30
Location: Ireland
Concentration: Healthcare, Finance
In the figure above, O is the center of the circle. Line AB intersects  [#permalink]

Show Tags

New post 25 Nov 2017, 10:25
Bunuel wrote:
Image
In the figure above, O is the center of the circle. Line AB intersects the circle only at point B, and line DC intersects the circle only at point C. If the circle has radius of 2, then AC =

(A) 4
(B) 2√2
(C) 4 + √2
(D) 4 + √3
(E) 2 + 2√2


Attachment:
The attachment 2017-11-23_2025_001.png is no longer available


ABO is a right isosceles triangle, hence \(BO = AB = r = 2\), hence the side AO = \(2\sqrt{2}\). \(AO + r = 2\sqrt{2} + 2\). The answer is E
Attachments

circle.jpg
circle.jpg [ 20.66 KiB | Viewed 811 times ]

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1978
Premium Member CAT Tests
Re: In the figure above, O is the center of the circle. Line AB intersects  [#permalink]

Show Tags

New post 25 Nov 2017, 11:04
Bunuel wrote:
Image
In the figure above, O is the center of the circle. Line AB intersects the circle only at point B, and line DC intersects the circle only at point C. If the circle has radius of 2, then AC =

(A) 4
(B) 2√2
(C) 4 + √2
(D) 4 + √3
(E) 2 + 2√2

Attachment:
The attachment 2017-11-23_2025_001.png is no longer available

Attachment:
ccccc.png
ccccc.png [ 16.4 KiB | Viewed 791 times ]

The length of AC = (length of hypotenuse, AO, of an isosceles right triangle) + (radius, CO)

Find length of AO

Connect O with B
Point B is tangent, so the radius is perpendicular to line AB and creates a right angle at point B

The triangle hence is a 45-45-90 isosceles right triangle, with side lengths in ratio*
\(x: x: x\sqrt{2}\)

One leg, BO \(= x\) = radius = \(2\)
Other leg, AB = BO = \(x = r = 2\)
Hypotenuse, AO = \(x\sqrt{2}=\)\(2\sqrt{2}\)

Add segment CO to get length of AC

The rest of the length of AC is
CO = r = \(2\)

Length of AC = \(2\sqrt{2} + 2\)

Answer E

*OR Pythagorean theorem:
\(leg^2 + leg^2 = hypotenuse, h^2\)
\(2^2 + 2^2 = h^2\)
\(8 = h^2\)
\(\sqrt{4*2} = \sqrt{h^2}\)
\(h = 2\sqrt{2}\) = length of AO

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Re: In the figure above, O is the center of the circle. Line AB intersects &nbs [#permalink] 25 Nov 2017, 11:04
Display posts from previous: Sort by

In the figure above, O is the center of the circle. Line AB intersects

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

Events & Promotions

PREV
NEXT


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®.