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555-605 Level|   Geometry|      
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MathRevolution
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What is the area of the region AOB shaded shown as above? Updated on: 08 Jun 2018, 08:19
Originally posted by MathRevolution on 08 May 2017, 03:04.
Last edited by MathRevolution on 08 Jun 2018, 08:19, edited 1 time in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

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66% (01:16) correct 34% (01:24) wrong based on 241 sessions

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There is a circle with the center O as above. What is the area of the sector AOB?

1) \(∠AOB=120^o\)
2) \(AB=50\)
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C
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What is the area of the region AOB shaded shown as above? 10 May 2017, 01:28
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==> 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
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What is the area of the region AOB shaded shown as above? 10 May 2017, 10:13
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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
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imnareshk
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What is the area of the region AOB shaded shown as above? 10 May 2017, 10:30
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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

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What is the area of the region AOB shaded shown as above? 20 May 2017, 02:46
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My take is E
It has to be explicitly mentioned that O is the center of the circle !!!!!!
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What is the area of the region AOB shaded shown as above? 07 May 2018, 15:33
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MathRevolution
Attachment:
5.8.png

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

1) \(∠AOB=120^o\)
2) \(AB=50\)

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 :thumbup:
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What is the area of the region AOB shaded shown as above? 05 Jul 2019, 05:27
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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
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What is the area of the region AOB shaded shown as above? 11 Jul 2019, 11:19
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ShivamoggaGaganhs
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



The way you wrote the formula is hard to understand. What does sqrt mean?
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What is the area of the region AOB shaded shown as above? 11 Jul 2019, 18:22
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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?
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What is the area of the region AOB shaded shown as above? 11 Jul 2019, 21:37
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JS1290
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?

AB is NOT a diameter. A diameter of a circle goes through the center. AB in the figure does not go through O.
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What is the area of the region AOB shaded shown as above? 12 Jul 2019, 00:36
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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
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What is the area of the region AOB shaded shown as above? 12 Jul 2019, 02:46
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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.
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What is the area of the region AOB shaded shown as above? 12 Jul 2019, 03:25
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kironk
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.


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

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