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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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Updated on: 11 Jul 2019, 05:43
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55% (hard)

Question Stats:

57% (01:16) correct 43% (01:44) wrong based on 116 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

Attachment:

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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15 May 2017, 20:11
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:
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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17 May 2017, 03:43
1
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 $$1: \sqrt{3}$$

$$Area(triangle)=a^2*\frac{√3}{{4}}$$

$$Radius = a* \frac{√3}{{3}}=2$$

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 [ 79.22 KiB | Viewed 8699 times ]

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"Be challenged at EVERY MOMENT."

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

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14 May 2017, 12:49
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 8879 times ]

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

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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!
Intern
Joined: 30 Mar 2017
Posts: 36
Location: United States (FL)
Re: An equilateral triangle is inscribed in a circle, as shown above. What  [#permalink]

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

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