Equilateral triangle

[szDave]

Hello,

The given answer is wrong, and I don't understand why! the diameter should be between 8*3^(1/2) <d< 2*8

[Tommy Wallach]

Hey SzDave,

To answer this question correctly, you need to have a solid understanding of arc lengths. Because this is an equilateral triangle, all three of the bulgy circular bits (the arcs between AB, BC, and AC) must be the same. So when they tell you that arc ABC is 24, that means two of the bulgy bits add up to 24. So each one is 12. That means the full circumference of the circle is 36.

Circumference = 2 * pi * r = 36 --> pi * r = 18 --> r = a little less than 6

So diameter is a bit less than 12. The closest answer choice is 11.

Let me know if that makes sense!

-t

[Lifetron]

2/3rd of the circumference (Arc ABC) = 24
So, Circumference = 36
2*3.14*r = 36
2*r = diameter = 36/3.14
Diameter ~ 11 [Closest]

So, Answer is 11 !