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# Geometry- triangle inscribed in a circle

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Intern
Joined: 28 Nov 2013
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Geometry- triangle inscribed in a circle [#permalink]

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13 Jan 2014, 23:29
What is the área of an equilateral triangle inscribed in a circle?

1) the area outside the triangle is 3Π
2) radius of the circle is 6

???

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Manager
Joined: 23 Jun 2008
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Re: Geometry- triangle inscribed in a circle [#permalink]

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14 Jan 2014, 00:24
UlisesOrdonez wrote:
What is the área of an equilateral triangle inscribed in a circle?

1) the area outside the triangle is 3Π
2) radius of the circle is 6

???

length and height of each side of the triangle can be written in terms of r using the Isosceles Triangle from the center of the circle to any two corners of triangle (angles: 120, 30 30)

given this, the area of triangle can be written in terms of r and also we know area of circle in terms of r that is pi*r^2 - so we should assess each option if it is sufficient to identify what r is

if (1) is known r can be calculated, since the area outside the triangle is difference of two figures that can be written in terms of r and subsequently we can calculate the area of the triangle. (1) alone is sufficient

if (2) using r we can calculate the area of triangle since we know length of each side and height in terms of r. (2) alone is sufficient.

Also note that we can answer DS questions without actually solving the question, we just need to prove if the data given in 1/2 are sufficient or not.
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Last edited by code19 on 23 Jan 2014, 22:31, edited 1 time in total.

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Intern
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Re: Geometry- triangle inscribed in a circle [#permalink]

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14 Jan 2014, 07:57
Thanks a lot! It was really helpful!!!

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Re: Geometry- triangle inscribed in a circle [#permalink]

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14 Jan 2014, 21:42
UlisesOrdonez wrote:
What is the área of an equilateral triangle inscribed in a circle?

1) the area outside the triangle is 3Π
2) radius of the circle is 6

???

When an equilateral triangle is inscribed in a circle, Side of the triangle = √3 * Radius of the circle
$$s = \sqrt{3}r$$

Area of circle $$=pi*r^2$$
Area of triangle $$= \sqrt{3}s^2/4 = 3\sqrt{3}r^2/4$$

Statement 1:
Area outside the triangle $$=pi*r^2 - 3\sqrt{3}r^2/4 = 3*pi$$
You can get r from here and subsequently the area of the triangle

Statement 2:
r is given directly so you can get the area of the triangle.

Here are some posts on circles and polygons inscribed in them.
http://www.veritasprep.com/blog/2013/06 ... d-circles/
http://www.veritasprep.com/blog/2013/07 ... relations/
http://www.veritasprep.com/blog/2013/07 ... other-way/
http://www.veritasprep.com/blog/2013/07 ... n-circles/
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Intern
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Re: Geometry- triangle inscribed in a circle [#permalink]

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16 Jul 2015, 21:37
The side of the triangle should be = √2* Radius of the circle, since we have an isosceles triangle with sides r and hypotenuse which is the side of the equilateral triangle

D

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Re: Geometry- triangle inscribed in a circle   [#permalink] 16 Jul 2015, 21:37
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