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ΔABC, which is right-angled at B, is inscribed in a circle with centre
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28 May 2019, 09:13

1

6

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

55% (02:46) correct 45% (02:56) wrong based on 76 sessions

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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

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

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.

Re: ΔABC, which is right-angled at B, is inscribed in a circle with centre
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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
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26 Feb 2020, 21:16

1

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.

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.
_________________

Prosper!!! GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha) e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi Click Here for Uneditable GOOGLE reviews

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

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

Good method. I feel jealous already.
_________________

Prosper!!! GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha) e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi Click Here for Uneditable GOOGLE reviews

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