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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
In the figure above, equilateral triangle ABC is inscribed in the
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06 Dec 2022, 00:11
06 Dec 2022, 00:11
Expert Reply
00:00
Question Stats:
72% (01:37) correct
27% (02:34) wrong based on 11 sessions
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In the figure above, the equilateral triangle ABC is inscribed in the circle. If the length of arc ABC is 24, what is the approximate diameter of the circle?
A. 5
B. 8
C. 11
D. 15
E. 19
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Attachment:
Circle.JPG [ 3.48 KiB | Viewed 1977 times ]
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: In the figure above, equilateral triangle ABC is inscribed in the
[#permalink]
08 Dec 2022, 09:17
08 Dec 2022, 09:17
Expert Reply
Triangle ABC = 24, and is an equilateral, so each side is 8. Since AB = 8, and does not go across the radius, the circumference of the circle is greater than 8. So you can then eliminate answer choices A and B. You are left with C (11), D (15) and E (19). Answer choice D, 15, is almost twice the length of AB. That almost certainly makes it too large of a number - thus you can rule out D and E. And you are left with C.
Answer: C
Answer: C
Re: In the figure above, equilateral triangle ABC is inscribed in the
[#permalink]
09 Dec 2022, 13:53
09 Dec 2022, 13:53
1
I solved it the following way:
If arc ABC = 24 and the triangle is equilateral, then arc AB = arc BC = arc CA
Therefore, Arc AB = 12 and circumference = 36
So, 36 = pi*diameter
diameter = 36/3.14 = a little more than 11
If arc ABC = 24 and the triangle is equilateral, then arc AB = arc BC = arc CA
Therefore, Arc AB = 12 and circumference = 36
So, 36 = pi*diameter
diameter = 36/3.14 = a little more than 11
