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](https://gre.myprepclub.com/forum/download/file.php?mode=view&id=224&sid=9902127f53d8fe78886f60f8e5febd2e)
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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