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# In the figure above, point O is the center of the circle and

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Re: In the figure above, point O is the center of the circle and [#permalink]

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29 Dec 2014, 21:09
How are we getting different variables x and y when the sides are equal. Can you explain Krishna. Cause three sides are equal shouldn't their angles be noted with the same variable?

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Re: In the figure above, point O is the center of the circle and [#permalink]

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29 Dec 2014, 21:14
I must have overlooked something because I get:

x+x+(180-2y)+y= 180
2x-y=0
2x-2x= 0[/quote]

Ignore the highlighted step.
after 2x - y = 0, when you take y to the other side, you get
2x = y

Without doing this step, how did you substitute 2x for y in the highlighted step?[/quote]
I see what I did. Below was my thought process:

x+x+(180-2y)+y= 180
2x-y=0 I then looked at the graph and applied the sum of two interior angles is equal to the opposite exterior which you labeled y. Once I got 2x= y I then went back to x+x+(180-2y)+y= 180 and thought I would end up with 5x= 180 but instead kept getting 2x-2x= 0

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Re: In the figure above, point O is the center of the circle and [#permalink]

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29 Dec 2014, 21:20
bankerboy30 wrote:
How are we getting different variables x and y when the sides are equal. Can you explain Krishna. Cause three sides are equal shouldn't their angles be noted with the same variable?

Note the sides that are equal
OC = AC = AB

OC and AC are sides if a triangle and the angles opposite to them are marked as x each (i.e. they are equal)

AC and AB are equal sides of another triangle and angles opposite to them are marked as y each. Note that you cannot mark them as x too because they are equal angles in a different triangle. Their measure could be different from x. I have explained this in detail in a post given below. Giving the explanation here:

"When two sides of a triangle are equal, the two opposite angles are equal. But can you say what the two angles are? No. Say a triangle has two sides of length 5 cm each. Do we know the measure of equal angles? No. They could be 40-40 or 50-50 or 80-80 etc. So if you have two different triangles with 2 sides of length 5 cm each, the equal angle could have different measures - in one triangle the equal angles could be 50-50, in the other triangle, the equal angles could be 70-70.

In triangle OAC, since OC = AC, you have two equal angles as x each. The third angle here is 180 - 2x.

In triangle ACB, since AC = AB, angle ACB = angle ABC but what makes you say that they must be x each too? This is a different triangle. Even if the sides have the same length as the sides of triangle OAC, there is no reason to believe that the equal angles need to be x each. So you call the angles y. The third angle here is 180 - 2y."
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17819 [0], given: 235 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7738 Kudos [?]: 17819 [1], given: 235 Location: Pune, India Re: In the figure above, point O is the center of the circle and [#permalink] ### Show Tags 29 Dec 2014, 21:25 1 This post received KUDOS Expert's post GMAT01 wrote: I see what I did. Below was my thought process: x+x+(180-2y)+y= 180 2x-y=0 I then looked at the graph and applied the sum of two interior angles is equal to the opposite exterior which you labeled y. Once I got 2x= y I then went back to x+x+(180-2y)+y= 180 and thought I would end up with 5x= 180 but instead kept getting 2x-2x= 0 From this equation: x+x+(180-2y)+y= 180, you derive that 2x = y. If you try to substitute 2x = y in this equation itself, you will just get 2x - 2x = 0 which implies 0 = 0. This equation has 2 variables and you need two distinct equations to get the value of the two variables. If both equations are just 2x = y, you cannot get the value of x. You need another equation to get the value of x. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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In the figure above, point O is the center of the circle and [#permalink]

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30 Dec 2014, 01:31
Algebra

x+x+180-y=180

2x+180-y=180 => 2x=y

so, x+2x+2x=180

5x=180 => x=36

Backsolving

take 34 (C)

34+34=68, y=68, 68*2=136, 180-136=44 not equal 34. We have to get higher value of X to make difference less (eliminate C,D,E)

go B (36)

36+36=72, y=72, 72*2=144, 180-144=36 (it is correct)

B

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In the figure above, point O is the center of the circle and [#permalink]

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18 May 2015, 07:50
What step am I doing wrong here? I can't figure it out. I don't understand how to go to 5x = 180

I just get to 4x + 180 - 4x = 180 aka 4x - 4x = 0..

edit: that last "8" kinda looks like a 5, but its supposed to be an 8

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Re: In the figure above, point O is the center of the circle and [#permalink]

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18 May 2015, 11:19
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erikvm wrote:
What step am I doing wrong here? I can't figure it out. I don't understand how to go to 5x = 180

I just get to 4x + 180 - 4x = 180 aka 4x - 4x = 0..

edit: that last "8" kinda looks like a 5, but its supposed to be an 8

Hi erikvm,

The angle which you have written as 180 - 2y = x because OA = OB (radii of the circle). So ∠OAB = ∠OBA.

∠(OAC + CAB) = y = 2x
x + ∠CAB = 2x which gives us ∠CAB = x.

Now summing up the angles in triangle OAB, we get x + 2x + 2x = 180 i.e. x = 36

Hope this helps

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Harsh
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In the figure above, point O is the center of the circle and [#permalink]

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25 Jul 2015, 19:40
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DropBear wrote:

Geometry: What is the angle of x?

Attachment:
The attachment Capture.PNG is no longer available

In the figure above, point O is the center of the circle and OC = AC = AB. What is the value of x?

A. 40
B. 36
C. 34
D. 32
E. 30

I had to guess this one recently and even after reading the official answer and explanation there are still some inferences that I just don't understand. I am really looking forward to seeing a few different ways of solving. Personally this is one of the hardest questions I have faced... Maybe you will find it easy

The reason for the poll is I would like to see how difficult everyone finds this question. As I said, this one really beat me!

Would be great to receive my first Kudos if you find this useful too

Straightforward question if you realize the additional constraint would come from the fact that in Triangle AOB, OA = OB = radius of the circle.

Now in triangle, ACO , $$\angle{COA} = \angle{OAC} = x$$ (as OC = AC) and $$\angle{ACB} = 2x$$ (external angle of a triangle)

Additionally, $$\angle{ACB}= \angle{ABC}$$ = 2x (as AC = AB)

FInally, in triangle AOB, OA = OB = radius of the circle ---> $$\angle{OBA}=\angle{OAB}$$ = 2x ---> $$\angle{CAB} =x$$

Thus , in triangle ACB,

$$\angle{ACB} + \angle{CBA} + \angle{BAC}$$ =2x+2x+x = 180 ---> x = 36. B is the correct answer.

Please search for a question before posting.

Merged the posts.
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In the figure above, point O is the center of the circle and [#permalink]

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08 Sep 2015, 01:40
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the measure of the exterior angle is equal to the sum of the two non-adjacent angles of the triangle --> Angle ACB=2x
OA=OB => 180-4x+x=2x; X=36°
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Re: In the figure above, point O is the center of the circle and [#permalink]

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03 Oct 2015, 11:17
Something it's not quite right here.

I'm also stuck with the last calculation.

STEP 1
180-2x + y = 180
2x = y OK I KNOW HOW TO FIND THIS

STEP 2
Then I convert Y to become 2X
<AOB = x
<ABO = 2x
<BAO = x + (180-4x)-----Why I add x to 180-4x because that's how I think we get a straight line of 180 degree

therefore:
x + 2x + x + (180-4x) = 180
then I get 180 = 180

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Re: In the figure above, point O is the center of the circle and [#permalink]

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04 Oct 2015, 23:37
1
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Expert's post
blendercroix wrote:
Something it's not quite right here.

I'm also stuck with the last calculation.

STEP 1
180-2x + y = 180
2x = y OK I KNOW HOW TO FIND THIS

STEP 2
Then I convert Y to become 2X
<AOB = x
<ABO = 2x
<BAO = x + (180-4x)-----Why I add x to 180-4x because that's how I think we get a straight line of 180 degree

therefore:
x + 2x + x + (180-4x) = 180
then I get 180 = 180

After step 2,
<BAO = <ABO
x + 180 - 4x = 2x
x = 36

The reason your third step doesn't work is because you used the property of total sum of triangle = 180 to get the relations. Now you are putting the relations back in sum of triangles is 180. You cannot get a value for x in this case. You need to put the relations in another property to arrive at a new conclusion (value of x).
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17819 [1], given: 235 Intern Status: Current Student Joined: 27 Mar 2014 Posts: 19 Kudos [?]: 19 [0], given: 9 Location: Bangladesh Concentration: Entrepreneurship, Finance GMAT 1: 520 Q39 V22 GMAT 2: 700 Q47 V38 Re: In the figure above, point O is the center of the circle and [#permalink] ### Show Tags 09 Feb 2016, 01:09 Here, since OC=CA, angle OAC=x. Hence angle ACB=2x and ABC=2x If we extend BO to Q, then we get an inscribed angle AQB which is half the central angle x. and the angle QAB=90 so, x/2+2x+90=180 5x/2=90 x=36 Attachments og QR 162.png [ 8.6 KiB | Viewed 5214 times ] Kudos [?]: 19 [0], given: 9 Intern Joined: 21 Sep 2015 Posts: 2 Kudos [?]: 5 [0], given: 5 Re: In the figure above, point O is the center of the circle and [#permalink] ### Show Tags 18 Jul 2016, 10:36 OA=OB (radius) Therefore angle oab = angle oba oc=ac(given) therefore angle aoc = angle cao therefore, angle oac = x degrees angle acb = 2x degrees (because exterior angle =sum of remote interior angles) ac=ab therefore angle abc = 2x degrees(isosceles triangle rule) ao=pb therefore, angle oab = 2x(proved before that angle abo =2x --->isosceles triangle rule) triangle aob =180 = 2x+2x+x= 5x=180 therefore x= 36 therefore answer is B Kudos [?]: 5 [0], given: 5 Senior Manager Status: Professional GMAT Tutor Affiliations: AB, cum laude, Harvard University (Class of '02) Joined: 10 Jul 2015 Posts: 423 Kudos [?]: 504 [0], given: 56 Location: United States (CA) Age: 37 GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GRE 1: 337 Q168 V169 WE: Education (Education) Re: In the figure above, point O is the center of the circle and [#permalink] ### Show Tags 09 Nov 2016, 20:36 Top Contributor 1 This post was BOOKMARKED Attached is a visual that should help. Attachments Screen Shot 2016-11-09 at 7.34.09 PM.png [ 241.73 KiB | Viewed 4042 times ] _________________ Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and via Skype, since 2002. McElroy Tutoring Kudos [?]: 504 [0], given: 56 Manager Joined: 17 Nov 2013 Posts: 181 Kudos [?]: 37 [0], given: 19 In the figure above, point O is the center of the circle and [#permalink] ### Show Tags 20 Nov 2016, 08:43 Hi Engr2012, I was about to post the same logic as you described. what I like about this method is how easy you get to the answer. For anyone else trying to answer this question and in search for optimization. Take a look at Engr2012 post and my graph. Attachments Capture.PNG [ 327.56 KiB | Viewed 4018 times ] Kudos [?]: 37 [0], given: 19 Manager Joined: 03 Jan 2017 Posts: 197 Kudos [?]: 9 [0], given: 4 Re: In the figure above, point O is the center of the circle and [#permalink] ### Show Tags 23 Mar 2017, 07:42 I loved this question! take a look at the triangle properties: if 2 sides are equal-then angles too so as oc=ac means that AOC=OAC x or AOB=180-2y as AC=AB -> ABC=ACB->CAB is x this means that angles OAB is made up of x + x=y so x=180-2(2x)->5x=180, x=36 Kudos [?]: 9 [0], given: 4 Intern Joined: 24 Feb 2017 Posts: 39 Kudos [?]: 1 [0], given: 0 Re: In the figure above, point O is the center of the circle and [#permalink] ### Show Tags 18 May 2017, 03:10 VeritasPrepKarishma wrote: tonebeeze wrote: In the figure attached, point O is the center of the circle and OC = AC = AB. What is the value of x (in degrees)? a. 40 b. 36 c. 34 d. 32 e. 30 A small diagram helps: Attachment: Ques1.jpg In the figure, you see (180 - 2x) + y = 180 (straight angle) so 2x = y Also, the moment you see the circle and its two radii, mark them equal and the corresponding angles equal. (the red angle = blue angle) x + 180 - 2y = y 5x = 180 (from above, y = 2x) x = 36 good explanation but I am not understand (the red angle=blue angle )? Kudos [?]: 1 [0], given: 0 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7738 Kudos [?]: 17819 [1], given: 235 Location: Pune, India Re: In the figure above, point O is the center of the circle and [#permalink] ### Show Tags 18 May 2017, 05:03 1 This post received KUDOS Expert's post mkumar26 wrote: VeritasPrepKarishma wrote: tonebeeze wrote: In the figure attached, point O is the center of the circle and OC = AC = AB. What is the value of x (in degrees)? a. 40 b. 36 c. 34 d. 32 e. 30 A small diagram helps: Attachment: Ques1.jpg In the figure, you see (180 - 2x) + y = 180 (straight angle) so 2x = y Also, the moment you see the circle and its two radii, mark them equal and the corresponding angles equal. (the red angle = blue angle) x + 180 - 2y = y 5x = 180 (from above, y = 2x) x = 36 good explanation but I am not understand (the red angle=blue angle )? OA and OB are radii of the same circle so they will be equal. So in triangle OAB, angle OAB = OBA ie. red angle = blue angle (in my diagram) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: In the figure above, point O is the center of the circle and [#permalink]

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25 May 2017, 11:35
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
In the figure above, point O is the center of the circle and OC = AC = AB. What is the value of x ?

(A) 40
(B) 36
(C) 34
(0) 32
(E) 30

Problem Solving
Question: 162
Category: Arithmetic Statistics
Page: 83
Difficulty: 600

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We know that OB and OA are radii of the circle, so their lengths are equal. And since OC = AC, we can denote their respective angles with x. For the supplementary angle of AC, we can use y and determine that 180-2x + y = 180 or 2x = y.

We also know that angle OAB = y, so x + 180 - 2y = y and thus x + 180 - 4x = 2x

-3x + 180 = 2x
180 = 5x

x = 36.

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Re: In the figure above, point O is the center of the circle and [#permalink]

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30 Jul 2017, 09:10
Very tough question. A key is recognizing that since OB is a radius and OA is a radius therefore angle OAB = angle OBA. The rest is also very tricky. Attached is a diagram.
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Re: In the figure above, point O is the center of the circle and   [#permalink] 30 Jul 2017, 09:10

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