|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 29 May 2008
Posts: 113
|
If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
 07 Sep 2009, 07:19
4
This post received
KUDOS
10
This post was
BOOKMARKED
D
E
Question Stats:
64% (02:34) correct
36% (01:22) wrong based on 686 sessions
HideShow timer Statistics
Attachment: 
Circle - original.PNG [ 3.31 KiB | Viewed 17193 times ]
If A is the center of the circle shown above and AB = BC = CD, What is the value of x? A. 15 B. 30 C. 45 D. 60 E. 75
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 21 Sep 2013, 13:18, edited 2 times in total.
Edited the question, added the diagram and added the OA
|
|
|
|
|
|
Intern
Joined: 03 Sep 2009
Posts: 29
|
Re: Weird cricle [#permalink]
Show Tags
07 Sep 2009, 18:10
A is the center of the circle => AB= AD = AC = BC = CD => ABC is a regular triangle => x = 30° The answer is B TheRob wrote: If A is the center of the circle shown above (see attachment) and AB = BC = CD, What is the value of x?
A) 15
B) 30
C) 45
D) 60
E) 75
(I tried to draw it the best I could sorry for the inconvenience)
|
|
|
|
|
|
Senior Manager
Joined: 20 Mar 2008
Posts: 452
|
Re: Weird cricle [#permalink]
Show Tags
07 Sep 2009, 18:49
8
This post received
KUDOS
1
This post was
BOOKMARKED
Triangle abc is equilateral, therefore all angles are 60. abc = acb = bac = 60.
Similarly, Triangle adc is equilateral, therefore all angles are 60. adc = acd = dac = 60.
Now, angle bad = bac + dac = 120, since each triangle is a reverse image of the other.
Now triangle bad is isosceles, since ab = ad.
Therefore abd = adb = 30, since bad =120.
Hence, B
|
|
|
|
|
|
Senior Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 264
|
Re: Weird cricle [#permalink]
Show Tags
25 Feb 2012, 11:55
1
This post received
KUDOS
you can solve the question easily by knowing two important properties of square and rhombus. 1. diagonals bisect each other. 2. each diagonal forms a 90 degree angle with the other diagonal
_________________
press +1 Kudos to appreciate posts
Download Valuable Collection of Percentage Questions (PS/DS)
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 39614
|
Re: If A is the center of the circle shown above [#permalink]
Show Tags
25 Feb 2012, 12:41
8
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
TheRob wrote: If A is the center of the circle shown above (see attachment) and AB = BC = CD, What is the value of x? A. 15 B. 30 C. 45 D. 60 E. 75 Attachment: The attachment Circle - original.PNG is no longer available (I tried to draw it the best I could sorry for the inconvenience) Look at the diagram below: Attachment: 
Circle.PNG [ 26.39 KiB | Viewed 17481 times ]
Given that AB = BC = CD, also since AB is the radius then AB = AC = AD = radius, so we have that: AB = BC = CD = AC = AD, so basically we have two equilateral triangles ABC and ACD with common base of AC (ABC and ACD are mirror images of each other). Line segment BD cuts the angle ABC in half and since all angles in equilateral triangle equal to 60 degrees then x=60/2=30 degrees. Answer: B.
_________________
New to the Math Forum?
Please read this: 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
Joined: 16 Dec 2011
Posts: 49
GMAT Date: 04-23-2012
|
Re: If A is the center of the circle shown above [#permalink]
Show Tags
27 Feb 2012, 08:25
bunuel ,
how can we say that line segment BD cuts the angle ABC in half which property is this , can u expalin me?
thanks
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 39614
|
Re: If A is the center of the circle shown above [#permalink]
Show Tags
27 Feb 2012, 08:42
pbull78 wrote: bunuel ,
how can we say that line segment BD cuts the angle ABC in half which property is this , can u expalin me?
thanks ABC and ACD are two equilateral triangles, which are mirror images of each other if you join vertices B and D, the segment BD must cut AC, the common base, in half. Which makes BD perpendicular bisector of AC --> so BO is a hight, median, and bisector of angle ABC (O being intersection point of BD and AC). Hope it's clear.
_________________
New to the Math Forum?
Please read this: 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
|
|
|
|
|
|
Manager
Joined: 10 Feb 2012
Posts: 71
Location: India
Concentration: Marketing, Strategy
GPA: 3.45
WE: Marketing (Pharmaceuticals and Biotech)
|
Re: If A is the center of the circle shown above [#permalink]
Show Tags
27 Feb 2012, 08:43
This is a proper rhombus... and this is one of the property of rhombus... that they bisect the diagonals in half.. and the diagonals bisect the angles in half...
also Angle (DAC is 120 degree )
and Triangle DAC is an isosceles triangle.. with base BD... hence angle ABD is 30
|
|
|
|
|
|
Intern
Joined: 16 Dec 2011
Posts: 49
GMAT Date: 04-23-2012
|
Re: If A is the center of the circle shown above [#permalink]
Show Tags
28 Feb 2012, 11:10
thanks bunuel , i also appreciate the explanation given by jivana.
|
|
|
|
|
|
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1327
|
Re: Find X [#permalink]
Show Tags
07 Apr 2012, 22:32
In triangle ABC, AB = BC = AC meaning all angles = 60 deg each. Similarly, in Triangle CDA, AD = CD = AC meaning all angles = 60 deg each. thus, in quadrilateral ABCD, Angle A = 120 = C and Angle B = 60 deg = Angle D. Thus in Triangle, ABC A + Angle ABD + Angle ADC = 180 120 + 2 * Angle ABD = 180 x = 30 deg.
_________________
Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!
|
|
|
|
|
|
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15927
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
28 Oct 2013, 09:42
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.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
|
|
|
|
|
|
Intern
Joined: 08 Oct 2011
Posts: 42
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
14 Nov 2013, 02:44
we are given that AB=BC=CD AB is the radius of the circle, so AB=AD This makes ABCD a square. Therefore, BD and AC are the diagonals of the square. Angle A, B, C, D = 90 and hence x=45 Why is this not considered that ABCD is a square?
Attachments
Circle.PNG [ 26.39 KiB | Viewed 12559 times ]
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 39614
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
14 Nov 2013, 02:49
|
|
|
|
|
|
Intern
Joined: 08 Oct 2011
Posts: 42
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
14 Nov 2013, 02:55
Bunuel wrote: aakrity wrote: we are given that AB=BC=CD
AB is the radius of the circle, so AB=AD
This makes ABCD a square. Therefore, BD and AC are the diagonals of the square. Angle A, B, C, D = 90 and hence x=45
Why is this not considered that ABCD is a square? ABCD is not a square it's a rhombus (the diagonals are not equal). O right how silly of me I assumed if a quadrilateral has four equal sides, it is a square. Now the solution makes sense to me. Thank you.
|
|
|
|
|
|
Current Student
Joined: 17 Oct 2013
Posts: 49
Location: India
Concentration: Strategy, Statistics
WE: Analyst (Computer Software)
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
22 Jun 2014, 09:38
Bunuel wrote: aakrity wrote: we are given that AB=BC=CD
AB is the radius of the circle, so AB=AD
This makes ABCD a square. Therefore, BD and AC are the diagonals of the square. Angle A, B, C, D = 90 and hence x=45
Why is this not considered that ABCD is a square? ABCD is not a square it's a rhombus (the diagonals are not equal). Bunnel, So Diagonals are 'angle bisectors' both in a Rhombus (not congruent here) and a Square. But it's not the case in a rectangle where they are congruent and perpendicular bosectors alone. Is my understanding accurate? I've read that every point on an angle bisector is equidistant from both the adjacent sides. Is there any other way to identify whether a diagonal is also an angle bisector? Thank you
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 39614
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
22 Jun 2014, 15:55
Kconfused wrote: Bunuel wrote: aakrity wrote: we are given that AB=BC=CD
AB is the radius of the circle, so AB=AD
This makes ABCD a square. Therefore, BD and AC are the diagonals of the square. Angle A, B, C, D = 90 and hence x=45
Why is this not considered that ABCD is a square? ABCD is not a square it's a rhombus (the diagonals are not equal). Bunnel, So Diagonals are 'angle bisectors' both in a Rhombus (not congruent here) and a Square. But it's not the case in a rectangle where they are congruent and perpendicular bosectors alone. Is my understanding accurate? I've read that every point on an angle bisector is equidistant from both the adjacent sides. Is there any other way to identify whether a diagonal is also an angle bisector? Thank you All is true, except that the diagonals in rectangle are no perpendicular to each other. They bisect each other but not at a right angle.
_________________
New to the Math Forum?
Please read this: 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
|
|
|
|
|
|
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15927
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
17 Sep 2015, 09:28
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.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
|
|
|
|
|
|
Intern
Joined: 06 Jul 2015
Posts: 15
Concentration: Entrepreneurship, Technology
GMAT 1: 690 Q50 V34 GMAT 2: 720 Q50 V38
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
13 Jan 2016, 04:12
Thought BC and CD were the arcs, not straight lines.
Please provide accurate diagrams of clarify in the statement.
|
|
|
|
|
|
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2642
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
13 Jan 2016, 05:48
|
|
|
|
|
|
Intern
Joined: 03 Oct 2015
Posts: 4
|
Re: If A is the center of the circle shown above (see attachment [#permalink]
Show Tags
22 Jun 2016, 22:37
What we know:
1) The figure is a rhombus (Diagonals are angular bisectors)
2) All lines extended from A are radii of the circle.
Therefore, AB = BC = AC. This in turn makes ABC an equilateral triangle. Now you know angleABC is 60*.
As the figure is a rhombus and its diagonals bisect the angleABC, x = 30
Answer : B
|
|
|
|
|
|
|
Re: If A is the center of the circle shown above (see attachment
[#permalink]
22 Jun 2016, 22:37
|
|
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
|
 10
|
 |
If the circles shown above are centered at the three vertices of a tri
|
Bunuel |
6 |
27 Sep 2016, 10:36 |
|
|
2
|
|
A circle passes through the center of a larger circle, as shown above.
|
Bunuel |
2 |
02 Sep 2016, 08:23 |
|
|
|
|
If the center of a circle lies on a smaller circle, as shown above, wh
|
reto |
3 |
27 Jun 2015, 18:15 |
|
|
5
|
|
If P is the center of the circle shown above, and BAC=30º, and the are
|
reto |
3 |
27 Jul 2016, 23:20 |
|
|
32
|
|
The circle with center C shown above is tangent to both axes
|
Walkabout |
17 |
30 May 2017, 16:26 |
|
|
|
|
|
|
