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An equilateral triangle is inscribed in a circle, as shown above. What

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An equilateral triangle is inscribed in a circle, as shown above. What  [#permalink]

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New post Updated on: 11 Jul 2019, 05:43
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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

Attachment:
2017-05-14_2305.png
2017-05-14_2305.png [ 7.85 KiB | Viewed 11533 times ]

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Originally posted by Bunuel on 14 May 2017, 12:06.
Last edited by SajjadAhmad on 11 Jul 2019, 05:43, edited 1 time in total.
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Re: An equilateral triangle is inscribed in a circle, as shown above. What  [#permalink]

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New post 15 May 2017, 20:11
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Bunuel wrote:
Image
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 \(1: \sqrt{3}\)


Attachment:
2017-05-14_2305.png


\(Area(triangle)=a^2*\frac{√3}{{4}}\)

\(Radius = a* \frac{√3}{{3}}=2\)

Answer : A
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Re: An equilateral triangle is inscribed in a circle, as shown above. What  [#permalink]

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New post 17 May 2017, 03:43
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ziyuen wrote:
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


laxpro2001 wrote:
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!


laxpro2001, Do refer the attachment.

https://gmatclub.com/forum/math-triangles-87197.html
Attachments

triangle.jpg
triangle.jpg [ 79.22 KiB | Viewed 8699 times ]


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Re: An equilateral triangle is inscribed in a circle, as shown above. What  [#permalink]

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New post 14 May 2017, 12:49
1
Bunuel wrote:
Image
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 \(1: \sqrt{3}\)


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


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
Attachments

Circle.png
Circle.png [ 5.76 KiB | Viewed 8879 times ]


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Re: An equilateral triangle is inscribed in a circle, as shown above. What  [#permalink]

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New post 17 May 2017, 03:38
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 \(1: \sqrt{3}\)


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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Re: An equilateral triangle is inscribed in a circle, as shown above. What  [#permalink]

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New post 18 May 2017, 02:47
Thank you, ziyuen
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Re: An equilateral triangle is inscribed in a circle, as shown above. What  [#permalink]

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Re: An equilateral triangle is inscribed in a circle, as shown above. What   [#permalink] 16 Oct 2018, 16:19
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