What is the area of the region AOB shaded shown as above?

Question

5.8.png There is a circle with the center O as above. What is the area of the sector AOB? 1) ∠AOB=120^o 2) AB=50

MathRevolution · Answer

==> In the original condition, you need to find the radius of the circle and the central angle, so there are 2 variable. In order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. 
By solving con 1) and con 2), the answer is C.

Answer: C

vivek2k70 · Answer

Can you let me know how did you solve this question.
How you come to know O is center of the circle.
I thought answer is E

imnareshk · Answer

1. Angle is 120°, however we would need the radius and something to find the area of triangle. So this statement is insufficient. 
2. Length of the chord is given here, however this statement alone is insufficient.

Combining both we would get the radius and subsequently the area of triangle.

So answer should be C

Sent from my MI 5 using  GMAT Club Forum mobile app

sleepynut · Answer

My take is E
It has to be explicitly mentioned that O is the center of the circle !!!!!!

22jadhavajit · Answer

Solution Statement 1: not sufficient, as we can not find anything from this. Statement 2: AB= 50 can not help us to find anything Statement 1+2: radius of the circle can be found using formula lengh(AB)=2(pi)r*angle/360. As triangle ABC forms isosceles triangle.... its height can be found out, and hence Area of ABC can be determined. Ans is C

ShivamoggaGaganhs · Answer

Area of an Isosceles triangle:

A=b/4(sqrt(4*a^2-b^2)

b---base
a--equal side

Combining we get both and b

MariemeDieng · Answer

The way you wrote the formula is hard to understand. What does sqrt mean?

JS1290 · Answer

Hi  chetan2u ,  Bunuel ,  VeritasKarishma ,

Could one of you experts please explain why option B is insufficient? Isnt there a rule that's something along the lines of the angle opposite is the diameter of the circle? So in our case angle 0= 90 degree and AB would be the diameter? Or can we not assume that AB is a diameter as it could be a chord merely?

Bunuel · Answer

AB is NOT a diameter. A diameter of a circle goes through the center. AB in the figure does not go through O.

saurabh9gupta · Answer

Not sure whether such question types are tested but one needs to know the below prop

1. the perpendicular from the center to any chord (line that connects any 2 points on the circle) will be a perpendicular bisector.

Once you know that you can drop a perpendicular bisector and then the big triangle gets divided into 2 smaller 30-60-90 triangle.

C

kironk · Answer

Bunuel , Can you please explain how C is sufficient? Statement (2) gives AB = 50, is this the length of the arc AB or chord AB. If it is the chord AB, I do not understand how C is sufficient.

Thanks in advance.

saurabh9gupta · Answer

The rule is side length opposite the angles as

30 - S
60 - S×(root 3)
90 - 2S

You know that the chord will bisect

So side opposite angle 60 is 25..
Rest you can solve once you get S

Posted from my mobile device

What is the area of the region AOB shaded shown as above?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards