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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
Expert Reply
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Question Stats:
83% (01:32) correct
16% (01:31) wrong based on 93 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.
