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# What is the measure of angle ACB in the circle above with center O?

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Math Expert
Joined: 02 Sep 2009
Posts: 51070
What is the measure of angle ACB in the circle above with center O?  [#permalink]

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09 Sep 2018, 07:07
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Difficulty:

35% (medium)

Question Stats:

66% (01:05) correct 34% (00:54) wrong based on 41 sessions

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What is the measure of angle ACB in the circle above with center O?

(1) The radius of the circle is 5.
(2) The length of the arc AB is 10.

Attachment:

image009.gif [ 1.95 KiB | Viewed 628 times ]

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Location: Pakistan
GMAT 1: 770 Q48 V50
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Re: What is the measure of angle ACB in the circle above with center O?  [#permalink]

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26 Sep 2018, 02:15
Looking at the diagram I can say that the angle ACB is 45° and I did not have to read any statement to get to this figure. Where am I wrong here Bunuel

I do not understand how do the values in the statements help.
_________________

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Posts: 931
WE: Supply Chain Management (Energy and Utilities)
What is the measure of angle ACB in the circle above with center O?  [#permalink]

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26 Sep 2018, 03:05
1
HinaTabassum wrote:
Looking at the diagram I can say that the angle ACB is 45° and I did not have to read any statement to get to this figure. Where am I wrong here Bunuel

I do not understand how do the values in the statements help.

Hi HinaTabassum,

We mustn't infer or conclude anything just looking at the diagram in GMAT(If specifically it's not mentioned).

Solution:-

In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc.

Here, AB is the intercepted arc, Angle AOB & Angle ACB are the measure of central angle and inscribed angle under arc AB respectively.

Refer the enclosed diagram, question stem : What is the measure of x ?

from st1, radius=5 & from st2, arc AB=10

So we can write Arc $$AB=2\pi*r(\frac{2x}{2\pi})$$
Or, $$10=2\pi*5(\frac{2*x}{2\pi})$$

We can solve the above equation and determine the value of 'x'.

Sufficient.

Ans. (C)

You may raise further queries(if any)
Attachments

Circle.gif [ 8.47 KiB | Viewed 347 times ]

_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

BSchool Forum Moderator
Joined: 23 May 2018
Posts: 274
Location: Pakistan
GMAT 1: 770 Q48 V50
GPA: 3.4
Re: What is the measure of angle ACB in the circle above with center O?  [#permalink]

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26 Sep 2018, 03:10
PKN wrote:
HinaTabassum wrote:
Looking at the diagram I can say that the angle ACB is 45° and I did not have to read any statement to get to this figure. Where am I wrong here Bunuel

I do not understand how do the values in the statements help.

Hi HinaTabassum,

We mustn't infer or conclude anything just looking at the diagram in GMAT(If specifically it's not mentioned).

Solution:-

In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc.

Here, AB is the intercepted arc, Angle AOB & Angle ACB are the measure of central angle and inscribed angle under arc AB respectively.

Refer the enclosed diagram, question stem : What is the measure of x ?

from st1, radius=5 & from st2, arc AB=10

So we can write Arc $$AB=2\pi*r(\frac{2x}{2\pi})$$
Or, $$10=2\pi*5(\frac{2*x}{2\pi})$$

We can solve the above equation and determine the value of 'x'.

Sufficient.

Ans. (C)

You may raise further queries(if any)

PKN I remember reading in many places that every diagram on the GMAT is drawn to scale.

I see how you solved it. I believe I relied on the pictionary here more than the numbers.
_________________

If you can dream it, you can do it.

Practice makes you perfect.

Kudos are appreciated.

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: What is the measure of angle ACB in the circle above with center O?  [#permalink]

### Show Tags

26 Sep 2018, 03:14
1
HinaTabassum wrote:
PKN wrote:
HinaTabassum wrote:
Looking at the diagram I can say that the angle ACB is 45° and I did not have to read any statement to get to this figure. Where am I wrong here Bunuel

I do not understand how do the values in the statements help.

Hi HinaTabassum,

We mustn't infer or conclude anything just looking at the diagram in GMAT(If specifically it's not mentioned).

Solution:-

In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc.

Here, AB is the intercepted arc, Angle AOB & Angle ACB are the measure of central angle and inscribed angle under arc AB respectively.

Refer the enclosed diagram, question stem : What is the measure of x ?

from st1, radius=5 & from st2, arc AB=10

So we can write Arc $$AB=2\pi*r(\frac{2x}{2\pi})$$
Or, $$10=2\pi*5(\frac{2*x}{2\pi})$$

We can solve the above equation and determine the value of 'x'.

Sufficient.

Ans. (C)

You may raise further queries(if any)

PKN I remember reading in many places that every diagram on the GMAT is drawn to scale.

I see how you solved it. I believe I relied on the pictionary here more than the numbers.

Hi HinaTabassum,

You may refer the below lines what test makers say:-

OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.

• All figures lie in a plane unless otherwise indicated.
https://gmatclub.com/forum/gmat-trick-r ... 01412.html

Hope this helps.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Manager
Joined: 10 Jan 2013
Posts: 156
Location: India
Concentration: General Management, Strategy
GMAT 1: 600 Q43 V30
GPA: 3.95
Re: What is the measure of angle ACB in the circle above with center O?  [#permalink]

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26 Sep 2018, 03:31
Here none of the statements are sufficient.

We will have to combine both the statements

Now if we join OB then
OA = OB = OC = 5

one can calculate angle AOB

(THETA/360)* 2*PI*R = 10.

angles can be calculated so C

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BSchool Forum Moderator
Joined: 23 May 2018
Posts: 274
Location: Pakistan
GMAT 1: 770 Q48 V50
GPA: 3.4
Re: What is the measure of angle ACB in the circle above with center O?  [#permalink]

### Show Tags

26 Sep 2018, 04:08
PKN wrote:
HinaTabassum wrote:
PKN wrote:

Hi HinaTabassum,

We mustn't infer or conclude anything just looking at the diagram in GMAT(If specifically it's not mentioned).

Solution:-

In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc.

Here, AB is the intercepted arc, Angle AOB & Angle ACB are the measure of central angle and inscribed angle under arc AB respectively.

Refer the enclosed diagram, question stem : What is the measure of x ?

from st1, radius=5 & from st2, arc AB=10

So we can write Arc $$AB=2\pi*r(\frac{2x}{2\pi})$$
Or, $$10=2\pi*5(\frac{2*x}{2\pi})$$

We can solve the above equation and determine the value of 'x'.

Sufficient.

Ans. (C)

You may raise further queries(if any)

PKN I remember reading in many places that every diagram on the GMAT is drawn to scale.

I see how you solved it. I believe I relied on the pictionary here more than the numbers.

Hi HinaTabassum,

You may refer the below lines what test makers say:-

OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.

• All figures lie in a plane unless otherwise indicated.
https://gmatclub.com/forum/gmat-trick-r ... 01412.html

Hope this helps.

Thank you PKN for the help.
_________________

If you can dream it, you can do it.

Practice makes you perfect.

Kudos are appreciated.

Re: What is the measure of angle ACB in the circle above with center O? &nbs [#permalink] 26 Sep 2018, 04:08
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# What is the measure of angle ACB in the circle above with center O?

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