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GRE Math Challenge #134-The vertices of an equilateral

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sandy
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GRE Math Challenge #134-The vertices of an equilateral [#permalink] New post   Updated on: 20 Feb 2020, 16:15
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The vertices of an equilateral triangle are on a circle.

Quantity A
Quantity B
The length of a side of the triangle
The diameter of the circle


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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B

Originally posted by sandy on 15 May 2015, 11:36.
Last edited by Carcass on 20 Feb 2020, 16:15, edited 1 time in total.
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Re: GRE Math Challenge #134 [#permalink] New post   17 May 2015, 09:19
sandy wrote:
The vertices of an equilateral triangle are on a circle.

Quantity A: The length of a side of the triangle
Quantity B: The diameter of the circle


Something nice happens when we sketch this information and add a center and two radii.
Image

Notice that if we add the lengths of the two radii we get the DIAMETER.
So, we're now comparing the sum of the two radii with one side of the triangle.

Well, there's a nice triangle rule that says: the length of the 3rd side MUST BE less than the sum of the lengths of the other two sides.
So, when we examine the lower triangle (comprised of 2 radii and one side of the equilateral triangle), we know that the length of the side of the equilateral triangle MUST BE LESS than the sum of the two radii (aka the diameter)

Answer: B

Cheers,
Brent
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sirkhan108
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Re: GRE Math Challenge #134-The vertices of an equilateral [#permalink] New post   13 May 2020, 06:42
The height of an eqt. triangle : (Root of 3)/2 * a = 1.732/2 * a < a

The diameter from one edge to the opp. point on the diameter will be greater than a.

Thus B
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Re: GRE Math Challenge #134-The vertices of an equilateral [#permalink] New post   13 Jan 2023, 11:44
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: GRE Math Challenge #134-The vertices of an equilateral [#permalink]
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