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

Question

https://gmatclub.com/forum/download/file.php?id=43454 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. image009.gif

MsInvBanker · Answer

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.

PKN · Answer

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)

MsInvBanker · Answer

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.

PKN · Answer

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.

saurabh9gupta · Answer

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

MsInvBanker · Answer

Thank you PKN for the help.

bumpbot · Answer

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

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