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ΔABC, which is right-angled at B, is inscribed in a circle with centre

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ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 28 May 2019, 09:13
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ΔABC, which is right-angled at B, is inscribed in a circle with centre O and radius 6 units. If the length of the smaller arc between points A and B is 4π units, what is the length of line segment BC


A. 3
B. π
C. 3√3
D. 6
E. 2π
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 28 May 2019, 09:32
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AC is the diameter, length of AC=2*6=12
Circumference of the circle=2*pi*r=12*pi
Angle AOB=(4pi/12pi)*360=120
Angle OAB=Angle OBA= (180-120)/2=30

AC/sin90=BC/sin30
BC=AC/2=12/2=6



mangamma wrote:
ΔABC, which is right-angled at B, is inscribed in a circle with centre O and radius 6 units. If the length of the smaller arc between points A and B is 4π units, what is the length of line segment BC


A. 3
B. π
C. 3√3
D. 6
E. 2π

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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 01 Jun 2019, 22:01
It is confusing that they say the "smaller arc" in reference to arc AB, because it is actually longer than arc BC.
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 13 Feb 2020, 20:21
How can we say that AC is the diameter of the circle?
Kindly share if I am missing some basic here.
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 13 Feb 2020, 20:51
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aniketnsit90 wrote:
How can we say that AC is the diameter of the circle?
Kindly share if I am missing some basic here.


check this :
https://www.teachoo.com/5521/1097/Angle ... /Theorems/

So angle subtended by diamter at circumference is always 90 and viceversa.
Since angle B is 90(and point B is on circumference) , so it means the diameter subtended that angle.
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 26 Feb 2020, 12:42
Bunuel nick1816

Why can't the answer be 2π?

Total circumference is 12π
Arc AC = 6π
Arc AB = 4π
So Arc BC = 12π - 6π - 4π = 2π
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 26 Feb 2020, 12:56
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TarPhi wrote:
Bunuel nick1816

Why can't the answer be 2π?

Total circumference is 12π
Arc AC = 6π
Arc AB = 4π
So Arc BC = 12π - 6π - 4π = 2π

You are absolutely right. But the question asks for line segment BC , not Arc BC. Hope this clears your doubt.
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 26 Feb 2020, 19:50
couldn't solve the above problem. can anyone explain with detailed explanation, thank you.
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 26 Feb 2020, 20:36
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Satyavani wrote:
couldn't solve the above problem. can anyone explain with detailed explanation, thank you.


Satyavani Please watch the video for detailed explanation

aniketnsit90 Watch the video to understand the property why AC should be diameter

briantoth6 Watch the video to understand what a smaller arc (minor arc) means

nick1816 GMAT doesn't expect or want us to use trigonometry

ANswer: Option D



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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 26 Feb 2020, 20:53
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GMATinsight Brother i know. But if someone knows higher mathematics concepts, he/she can use it. It can save some time.



GMATinsight wrote:
Satyavani wrote:
couldn't solve the above problem. can anyone explain with detailed explanation, thank you.


Satyavani Please watch the video for detailed explanation

aniketnsit90 Watch the video to understand the property why AC should be diameter

briantoth6 Watch the video to understand what a smaller arc (minor arc) means

nick1816 GMAT doesn't expect or want us to use trigonometry

ANswer: Option D


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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 26 Feb 2020, 21:16
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nick1816 wrote:
GMATinsight Brother i know. But if someone knows higher mathematics concepts, he/she can use it. It can save some time.



GMATinsight wrote:
Satyavani wrote:
couldn't solve the above problem. can anyone explain with detailed explanation, thank you.


Satyavani Please watch the video for detailed explanation

aniketnsit90 Watch the video to understand the property why AC should be diameter

briantoth6 Watch the video to understand what a smaller arc (minor arc) means

nick1816 GMAT doesn't expect or want us to use trigonometry

ANswer: Option D




Happy to know that you are aware of it. :) :thumbup:

There are many misguided souls who don't. being an expert, I like to apprise people of facts here. I am sure you will take my previous comment and effort in a positive spirit.

Just another suggestion, try to minimize use of higher maths while you are practicing. It's a good advice. There are many genuine reasons which might not sound convincing and meritorious but the bottom line is GMAT should be taken as GMAC wants. and there is definitely some merit in the suggestion.

All the best and happy preparation. :)
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 26 Feb 2020, 23:08
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GMATinsight - thanks for the video.

I solved it slightly differently. Once you find angle AOB = 120 degrees and ABO and OAB is 30 degrees each, all you need to do is -
Angle COB is 60, Angle OBC is 60 therefore the 3rd angle is 60. Hence it is an equilateral triangle. Hence BC is 6
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 26 Feb 2020, 23:31
TarPhi wrote:
GMATinsight - thanks for the video.

I solved it slightly differently. Once you find angle AOB = 120 degrees and ABO and OAB is 30 degrees each, all you need to do is -
Angle COB is 60, Angle OBC is 60 therefore the 3rd angle is 60. Hence it is an equilateral triangle. Hence BC is 6


TarPhi That's a very good inference to make.

Good method. I feel jealous already. :-D
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre  [#permalink]

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New post 26 Feb 2020, 23:40
GMATinsight wrote:
TarPhi wrote:
GMATinsight - thanks for the video.

I solved it slightly differently. Once you find angle AOB = 120 degrees and ABO and OAB is 30 degrees each, all you need to do is -
Angle COB is 60, Angle OBC is 60 therefore the 3rd angle is 60. Hence it is an equilateral triangle. Hence BC is 6


TarPhi That's a very good inference to make.

Good method. I feel jealous already. :-D



Haha cheers man :) thanks again!
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Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre   [#permalink] 26 Feb 2020, 23:40
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