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The circle with center O has a circumference of
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13 Sep 2017, 12:46
13 Sep 2017, 12:46
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85% (01:31) correct
14% (01:22) wrong based on 84 sessions
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The circle with center O has a circumference of 12π \(\sqrt{3}\). If AC is a diameter of the circle, what is the length of line segment AB?
A. \(3 \sqrt{2}\)
B. 6
C. \(6 \sqrt{3}\)
D. 18
E. \(18 \sqrt{3}\)
_________________
Re: The circle with center O has a circumference of
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02 Mar 2018, 05:28
02 Mar 2018, 05:28
2
The circumference of the circle is 12*pi*sqrt(3).
So, diameter AC = 12*sqrt(3). According to 30-60-90 triangle rule, we got that 2*x= 12*sqrt(3) or, x=6*sqrt(3).
So, the length of the line segment AB=6*sqrt(3)
The answer is C.
So, diameter AC = 12*sqrt(3). According to 30-60-90 triangle rule, we got that 2*x= 12*sqrt(3) or, x=6*sqrt(3).
So, the length of the line segment AB=6*sqrt(3)
The answer is C.
Re: The circle with center O has a circumference of
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22 Aug 2020, 09:38
22 Aug 2020, 09:38
3
An important note to add onto YMAkib's explanation:
We know this is a 30-60-90 triangle because of the rule that "Any diameter of a circle subtends a right angle to any point on the circle. No matter where the point is, the triangle formed with diameter is always a right triangle." This tells us that <ABC is a right angle, and triangle ABC is a right triangle.
I learned this rule and others from greprepclub's math book.
We know this is a 30-60-90 triangle because of the rule that "Any diameter of a circle subtends a right angle to any point on the circle. No matter where the point is, the triangle formed with diameter is always a right triangle." This tells us that <ABC is a right angle, and triangle ABC is a right triangle.
I learned this rule and others from greprepclub's math book.
Re: The circle with center O has a circumference of
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22 Aug 2020, 10:42
22 Aug 2020, 10:42
1
Expert Reply
We do have also our math book
https://gre.myprepclub.com/forum/gre-math- ... -2609.html
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https://gre.myprepclub.com/forum/gre-math- ... -2609.html
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Re: The circle with center O has a circumference of
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16 Nov 2021, 03:43
16 Nov 2021, 03:43
1
Start by finding the radius/diameter: if the circumference is 12pi*sqrt3, then this means pi*d = 12pi*sqrt3 or d = 12sqrt3.
Furthermore, if AC is a diameter, we know the angle at B to be 90 degrees. This means that the entire triangle is a 30-60-90 triangle with proportions x:xsqrt3:2x.
That means that, in this case, our x would be opposite the 30--that's the one we're looking for.
We know of course that the 2x, our AC, is 12sqrt3. This implies of course that x, our AB, is 6sqrt3.
_________________
Furthermore, if AC is a diameter, we know the angle at B to be 90 degrees. This means that the entire triangle is a 30-60-90 triangle with proportions x:xsqrt3:2x.
That means that, in this case, our x would be opposite the 30--that's the one we're looking for.
We know of course that the 2x, our AC, is 12sqrt3. This implies of course that x, our AB, is 6sqrt3.
_________________
GRE / GMAT Tutor London and Online since 2005. Writer, editor, contributor for test-prep materials.
Struggling with Permutations and Combinations (Combinatorics?). I've put loads of free resources here: https://privategmattutor.london/gmat-combinatorics-ultimate-guide-to-gmat-permutations-and-combinations/
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Struggling with Permutations and Combinations (Combinatorics?). I've put loads of free resources here: https://privategmattutor.london/gmat-combinatorics-ultimate-guide-to-gmat-permutations-and-combinations/
As ever, feel free to get in touch for impartial GRE / GMAT advice or to enquire about lessons at:
https://privategmattutor.london
Re: The circle with center O has a circumference of
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17 Jun 2023, 02:38
17 Jun 2023, 02:38
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