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Math Expert V
Joined: 02 Sep 2009
Posts: 56272
What is the measure of angle ACB in the circle above with center O?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 70% (01:19) correct 30% (01:20) wrong based on 49 sessions

### HideShow timer Statistics  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 752 times ]

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Joined: 23 May 2018
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Location: Pakistan
Re: What is the measure of angle ACB in the circle above with center O?  [#permalink]

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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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Practice makes you perfect.

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VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
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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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 465 times ]

_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Retired Moderator G
Joined: 23 May 2018
Posts: 487
Location: Pakistan
Re: What is the measure of angle ACB in the circle above with center O?  [#permalink]

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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.
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
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

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:-

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  G
Joined: 10 Jan 2013
Posts: 243
Location: India
Concentration: General Management, Strategy
GPA: 3.95
Re: What is the measure of angle ACB in the circle above with center O?  [#permalink]

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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

Posted from my mobile device
Retired Moderator G
Joined: 23 May 2018
Posts: 487
Location: Pakistan
Re: What is the measure of angle ACB in the circle above with center O?  [#permalink]

### Show Tags

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:-

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?   [#permalink] 26 Sep 2018, 05:08
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