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605-655 (Medium)|   Geometry|      
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Bunuel
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An equilateral triangle is inscribed in a circle, as shown above. What Updated on: 11 Jul 2019, 05:43
Originally posted by Bunuel on 14 May 2017, 12:06.
Last edited by Sajjad1994 on 11 Jul 2019, 05:43, edited 1 time in total.
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A
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59% (01:17) correct 41% (01:35) wrong based on 234 sessions

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An equilateral triangle is inscribed in a circle, as shown above. What is the area of the triangle?

(1) The radius of the circle is 2.
(2) The ratio of the radius of the circle to a side of the triangle is \(1: \sqrt{3}\)

Source: Nova GMAT
Difficulty Level: 700
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2017-05-14_2305.png
2017-05-14_2305.png [ 7.85 KiB | Viewed 21637 times ]
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A
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An equilateral triangle is inscribed in a circle, as shown above. What 17 May 2017, 03:43
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ziyuen
An equilateral triangle is inscribed in a circle, as shown above. What is the area of the triangle?

(1) The radius of the circle is 2.
(2) The ratio of the radius of the circle to a side of the triangle is \(1: \sqrt{3}\)

\(Area(triangle)=a^2*\frac{√3}{{4}}\)

\(Radius = a* \frac{√3}{{3}}=2\)

Answer : A
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laxpro2001
Can you please explain your triangle area formula. I get the area as being \(Area(triangle)=a^2*\frac{√3}{{2}}\)

Also can you please explain the your formula for radius? I tried calculating that but also got something different.

Thanks!
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laxpro2001, Do refer the attachment.

https://gmatclub.com/forum/math-triangles-87197.html
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triangle.jpg [ 79.22 KiB | Viewed 17662 times ]

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An equilateral triangle is inscribed in a circle, as shown above. What 14 May 2017, 12:49
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Bunuel

An equilateral triangle is inscribed in a circle, as shown above. What is the area of the triangle?

(1) The radius of the circle is 2.
(2) The ratio of the radius of the circle to a side of the triangle is \(1: \sqrt{3}\)


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The attachment 2017-05-14_2305.png is no longer available
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A

1. as per the attached figure, we can find s by using the following formulae:
s=2r * sin(theta/2)
sufficient

2. ratio neither tells us the side nor the radius.
insufficient
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Circle.png
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An equilateral triangle is inscribed in a circle, as shown above. What 15 May 2017, 20:11
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Bunuel

An equilateral triangle is inscribed in a circle, as shown above. What is the area of the triangle?

(1) The radius of the circle is 2.
(2) The ratio of the radius of the circle to a side of the triangle is \(1: \sqrt{3}\)


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Attachment:
2017-05-14_2305.png
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\(Area(triangle)=a^2*\frac{√3}{{4}}\)

\(Radius = a* \frac{√3}{{3}}=2\)

Answer : A
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An equilateral triangle is inscribed in a circle, as shown above. What 17 May 2017, 03:38
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An equilateral triangle is inscribed in a circle, as shown above. What is the area of the triangle?

(1) The radius of the circle is 2.
(2) The ratio of the radius of the circle to a side of the triangle is \(1: \sqrt{3}\)


Show Spoiler
Attachment:
2017-05-14_2305.png
[/quote]

\(Area(triangle)=a^2*\frac{√3}{{4}}\)

\(Radius = a* \frac{√3}{{3}}=2\)

Answer : A[/quote]

Can you please explain your triangle area formula. I get the area as being \(Area(triangle)=a^2*\frac{√3}{{2}}\)

Also can you please explain the your formula for radius? I tried calculating that but also got something different.

Thanks!
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laxpro2001
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An equilateral triangle is inscribed in a circle, as shown above. What 18 May 2017, 02:47
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Thank you, ziyuen
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An equilateral triangle is inscribed in a circle, as shown above. What 28 Dec 2019, 22:50
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Bunuel

An equilateral triangle is inscribed in a circle, as shown above. What is the area of the triangle?

(1) The radius of the circle is 2.
(2) The ratio of the radius of the circle to a side of the triangle is \(1: \sqrt{3}\)

Source: Nova GMAT
Difficulty Level: 700
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Side length of the triangle is required

(1) 30-60-90 triangle can be formed by dropping a perpendicular from center of the circle on the side of the triangle. Side length of the equilateral triangle can now be calculated as radius is known. Sufficient

(2) ratio of radius of circle to side length of the triangle is not sufficient to find side length as the ratio is already known from 30-60-90 triangle. Insufficient

Therefore, A is correct.
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An equilateral triangle is inscribed in a circle, as shown above. What 18 Mar 2023, 10:28
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