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

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Difficulty:   55% (hard)

Question Stats: 56% (01:17) correct 44% (01:44) wrong based on 111 sessions

HideShow timer Statistics 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 [ 7.85 KiB | Viewed 11453 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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1
Bunuel 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 $$1: \sqrt{3}$$

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 [ 5.76 KiB | Viewed 8802 times ]

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

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Bunuel 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 $$1: \sqrt{3}$$

Attachment:
2017-05-14_2305.png

$$Area(triangle)=a^2*\frac{√3}{{4}}$$

$$Radius = a* \frac{√3}{{3}}=2$$

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

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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 $$1: \sqrt{3}$$

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

$$Area(triangle)=a^2*\frac{√3}{{4}}$$

$$Radius = a* \frac{√3}{{3}}=2$$

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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3
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 $$1: \sqrt{3}$$

$$Area(triangle)=a^2*\frac{√3}{{4}}$$

$$Radius = a* \frac{√3}{{3}}=2$$

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 [ 79.22 KiB | Viewed 8622 times ]

_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

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

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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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