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

Question

https://gmatclub.com/forum/download/file.php?id=35201 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 2017-05-14_2305.png

gmatexam439 · Answer

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

BillyZ · Answer

Area(triangle)=a^2*\frac{√3}{{4}}

Radius = a* \frac{√3}{{3}}=2

Answer :  A

laxpro2001 · Answer

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

[/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!

BillyZ · Answer

laxpro2001 , Do refer the attachment.

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

laxpro2001 · Answer

Thank you,  ziyuen

QuantMadeEasy · Answer

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.

bumpbot · Answer

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

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