GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The circle with center O has a circumference of
[#permalink]
13 Sep 2017, 12:46
13 Sep 2017, 12:46
Expert Reply
00:00
Question Stats:
83% (01:32) correct
16% (01:37) wrong based on 105 sessions
Hide Show timer Statistics
Attachment:
circle.jpg [ 29.24 KiB | Viewed 7578 times ]
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
[#permalink]
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
[#permalink]
22 Aug 2020, 09:38
22 Aug 2020, 09:38
4
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.
